Ganesha is one of the most easily recognizable gods in the Hindu pantheon, known as the elephant-headed deity. He is usually praised with affection at the start of any Hindu ritual or ceremony and at the beginning of any writing. His elephantine representation has deeper symbolic meaning as Ganesha's large size represents his metaphysical ability to remove obstacles in his devotees' lives. Widely worshiped among Hindus as the lord of beginnings, Ganesha is honored as the patron of arts and sciences, intellect and wisdom.
Historically, Ganesha appeared as a distinct deity in recognizable form beginning in the fourth to fifth centuries C.E., during the Gupta Period (c. 320-600 C.E.) of Indian history. His popularity rose quickly, and he was formally included among the five primary deities of Smartism, an influential stream of Hinduism that began in the ninth century C.E. The principal scriptures dedicated to his worship are the Ganesha Purana, the Mudgala Purana, and the Ganapati Atharvashirsa. Ganesha is deeply beloved by Hindus around the world today, with many millions recognizing him as their Ishta devata, or "chosen divinity." 
In Hinduism, the worship of Ganesha is considered to be compatible with devotion to other deities, and various Hindu sects worship him regardless of their affiliations with other gods. In this capacity, Ganesha is a deity that overcomes religious sectarianism because virtually all Hindu groups agree to revere Ganesha, regardless of their particular affiliation. Thus, Ganesha can be seen as a remover of religious intolerance and intellectual exclusivism.
The name Ganesha derives from the Sanskrit words gana (meaning "a group") and isha (meaning "lord" or "master"), togther translated as "Lord of Hosts" - a familiar phrase to many Christians and Jews. 
Ganesha has many other titles and epithets, including most prominently Ganapati (meaning "lord of the group"), and Vignesha, (meaning "Lord of Obstacles"). The Sanskrit names Vighnakartā ("obstacle-creator") and Vighnahartā ("obstacle-destroyer") are also used to summarize the Ganesha's dual functions pertaining to obstacles. Another name employed in the Ganesha Purana and Ganesha Sahasranama is Buddhipriya or "lover of intelligence"
Some of Ganesha's epithets refer to his physical features. The earliest name referring to Ganesha is Ekadanta ("One Tusk"), referring to his single tusk; the other is broken off.  According to the Mudgala Purana two different incarnations of Ganesha use names based on Ganesha's paunch: Lambodara ("Pot Belly," or literally "Hanging Belly") and Mahodara ("Great Belly").
One of the main names for Ganesha in the Tamil language is Pille or Pillaiyar, which means "Little Child". A. K. Narain differentiates these terms by saying that pille means a "child" and pillaiyar a "noble child," and adds that the words pallu, pella, and pell in the Dravidian family of languages signify "tooth or tusk of an elephant" but more generally an elephant alone.  In discussing the name Pillaiyar, Anita Raina Thapan notes that since the Pali word pillaka has the significance of "a young elephant," it is possible that pille originally meant "the young of the elephant."
Ganesha appears as a distinct deity in clearly-recognizable form beginning in the fourth to fifth centuries C.E., suggesting the emergence of the Ganapatya (Ganesh-worshipping) sect (probably an offshoot of mainstream Shaivism). The earliest cult image of Ganesha so far known is found in the niche of the Shiva temple at Bhumra, which has been dated to the Gupta period. By about the tenth century C.E., Ganesha's independent cult had come into existence.
Despite these fragments of information, questions as to Ganesha's historical origin are still largely unanswered, and many theories persist as to how he came into being. One theory of Ganesha's origin states that he gradually came to prominence in connection with the four Vināyakas, from whom he gains one of his epithets (see above)  In Hindu mythology, the Vināyakas were a group of four troublesome demons who created obstacles and difficulties, but who were easily propitiated. Krishan is among the academics who accept this view, and states flatly that Ganesha "is a non-vedic god. His origin is to be traced to the four Vināyakas, evil spirits, of the Mānavagŗhyasūtra (seventh–fourth century B.C.E.) who cause various types of evil and suffering." While none of these gods are conceived to be elephant-headed, they are held to be responsible for the creation of obstacles.
Other scholars have interpreted the myths of Ganesha as revelatory of his status as a former totemic emblem. In this way, Ganesha's adoption by Shiva (see below) is a mythological illustration of syncretism, in which a tribe under the banner of the elephant is assimilated into the Brahmanic fold.  Numerous possibilities for this hypothesis have been suggested, including South India tribal traditions, the Pillayar caste, the Munda of central India, the Gajas of the northeast, and the Naga cult of Western India.  However, all these possibilities are problematic because there is no independent evidence for the existence of an elephant cult or a totem in any of these regions. 
Ganesha's rise to prominence was codified in the ninth century C.E. when he was formally included as one of the five primary deities of Smartism. The "worship of the five forms" (pañcāyatana pūjā) system, which was popularized by the ninth-century philosopher Śaṅkarācārya among orthodox Brahmins of the Smārta tradition, invokes the five deities Ganesha, Vishnu, Shiva, Devī, and Sūrya. It was instituted by Śaṅkarācārya primarily to unite the principal deities of the foremost sects of Hinduism at the time (Gāṇapatya, Śaiva, Vaiṣṇava, and Sūrya) by giving them equal status. The monistic philosophy preached by Śaṅkarācārya made it possible to choose any one of these figures as a preferred principal deity while at the same time worshiping the other four deities as different forms of the same all-pervading Brahman. This served to formalize the role of Ganesha as a complementary deity.
India had an impact on many countries throughout Asia as a result of commercial and cultural contacts. In particular, the period from approximately the tenth century C.E. onwards was marked by the development of new networks of exchange and a resurgence of money circulation throughout Asia, and it was during this time that Ganesha became the principal deity associated with traders. These traders prayed that the god would grant them success and remove obstacles in their path as they went outside of India to pursue commercial ventures; accordingly, the earliest inscriptions where Ganesha is invoked before any other deity were composed by the merchant community. Since Ganesha was widely worshipped by these enterprising travelers, he became one of the most prevalent Hindu deities in foreign lands.  As could be expected, the worship of Ganesha by Hindus outside of India shows much regional variation.
The gradual emigration of Hindus to Southeast Asia also established Ganesha in modified forms in mostly Buddhist nations such as Burma, Cambodia, and Thailand. In these nations Hinduism and Buddhism were practiced side-by-side, and mutual influences can be seen in Ganesha iconography in these regions. Among Buddhists in Thailand, for example, Ganesha maintained his traditional Hindu function as a remover of obstacles and is therefore considered a god of success. In Nepal, the Hindu form of Ganesha known as Heramba has traditionally been very popular, and is often depicted with five heads and riding upon a lion. Tibetan representations of Ganesha are usually more ambivalent in nature; in one Tibetan form he is shown being trodden underfoot by Mahākala, a popular Tibetan deity, while in other depictions he is shown as the Destroyer of Obstacles, sometimes dancing in jubilation over his successes. This dancing form, called Nṛtta Ganapati, originally gained popularity in North India and was later adopted in Nepal before arriving in Tibet. In Buddhism in general, Ganesha is seen not only as a benevolent deity, but also in the form of a demon called Vināyaka. Such images may be found among Buddhist sculptures of the late Gupta period.
Ganesha also spread into a wide variety of additional cultures. Hindus brought Ganesh with them to the Malay Archipelago, and statues to the deity can be found throughout the region in great numbers, often beside sanctuaries dedicated to Shiva  Before the arrival of Islam, Afghanistan had close cultural ties with India, and Afghans venerated both Hindu and Buddhist deities. A few examples of sculptures from the period fifth-seventh century C.E. have survived in this region, including some depicting Ganesha, suggesting that the worship of the deity was in vogue in the region at that time. Ganesha also appears in both China and Japan in forms that show distinct regional character. In North China, the earliest known stone statue of Ganesha carries an inscription dated 531 C.E.  while in Japan a cult dedicated to the deity was first mentioned in 806 C.E.
Ganesha as we know him today does not appear in the Vedas, at least not explicitly. Rg Veda 2.23.1 calls upon a deity also known as Ganapati, the "leader of hosts." While most devotees of Ganesha accept this as proof of their chosen deity's Vedic origin, scholars have suggested that this text is actually referring to Brhaspati, the teacher of the gods, rather than Ganesh. Similarly, the Yajur Veda invokes "one having a trunk," although this phrase is located within a larger litany to Rudra, Shiva's prototype.  Hence, this and other Vedic references to trunks and tusks are most likely referring in actuality to the elephantine features assumed by Shiva after he slayed an elephant demon.  Ganesha also does not appear in literature of the epic period, save for a brief passage in the Mahabharata in which he serves as Vyasa's scribe. However, this singular story is not accepted as part of the original text by the editors of the critical edition of the Mahabharata, where the twenty-line story is relegated to a footnote in an appendix.
It was not until the Puranas that Ganesha became an established figure in Hindu scripture. While the Puranas defy precise chronological ordering, the more detailed narratives of Ganesha's life appear in the later texts, circa 600–1300 C.E.  References to Ganesha occuring in Puranas predating this (such as those in the Vayu and Brahmanda Puranas), are considered to be later interpolations made during the seventh to tenth centuries C.E. Between the twelfth and fifteenth centuries, Ganesha also became the focal point of two Puranic texts of his own, the Ganesha Purana and the Mudgala Purana.  His pivotal role in these texts reflects Ganesha's acceptance as one of the five principal deities of Brahmanism and the subsequent development of the Ganapatya tradition in which some brāhmaṇas chose to worship Ganesha as their principal deity  These two scriptures, along with the Ganapati Atharvashirsa (a text composed during the sixteenth or seventeenth centuries C.E.) remain the core texts involved in devotion to Ganesha. 
In popular Hindu mythology, Ganesha is considered to be the son of the Hindu deity Shiva and Parvati. The most common account of his birth begins with Shiva leaving his wife Parvati for an extended period of time in order to meditate upon Mount Kailasa. This inspired intense loneliness within the goddess. Longing for a son, she gave birth to the young man, Ganesha. She quickly ordered him to stand guard at the door of her private chamber while she bathed. Eventually, Shiva returned from his meditation and attempted to access Parvati's private chamber. Ganesha refused to let him in and a struggle ensued, after which Shiva beheaded Ganesha. Hearing the commotion, Parvati came out of her bath and informed Shiva that he had just killed her child, and threatened to destroy the universe if the situation was not rectified. Shiva promptly sent his servants to the North, the holy direction, so that they could find a new head for Ganesha. Details as to where this replacement head came from vary according to different sources. Eventually, the servants found an elephant and cut off its head, which they placed upon Ganesh's shoulders upon their return. When Ganesh came back to consciousness, Shiva adopted him as his own. 
Puranic myths provide a wide variety of other explanations for Ganesha's form. Some texts say that he was actually born with his elephant head (or heads), though in most stories he acquires the head later.  In a different story, when Ganesha was born his mother Parvati showed off her new baby to the other gods. Unfortunately, the god Shani (a deity corresponding to the planet Saturn) – who is said to have the "evil eye" – looked at him, causing the baby's head to be burned to ashes. The god Vishnu came to the rescue and replaced the missing head with that of an elephant. In yet another story, Ganesha is created directly by Shiva's laughter. After Ganesha's birth, Shiva became concerned that the youth was excessively beautiful, and so he cursed Ganesha to have the head of an elephant and a protruding belly in order to make his appearance less appealing.
Along with his mother and father, Ganesh's closest kin includes a brother, Karttikeya (also known as Skanda) Prior to the emergence of Ganesha as a cult figure, Karttikeya had a long and glorious history as a martial deity from about 500 B.C.E. until approximately 600 C.E., when his worship declined significantly in North India in conjunction with the rise of Ganesha. Several stories relate episodes of sibling rivalry between Ganesha and Karttikeya, such as their competition over women,  which may reflect historical tensions between the respective sects.
Ganesha's marital status varies widely in mythological stories. One pattern of myths based in various Puranas associates Ganesha with the concepts of Buddhi (intellect), Siddhi (spiritual power), and Riddhi (prosperity), three qualities personified as goddesses who are considered to be Ganesha's wives.  In Chapter I.18.24-39 of the Ganesha Purana, Brahmā performs worship in honor of Ganesha. During the puja, Ganesha himself causes Buddhi and Siddhi to appear so that Brahmā can offer them back to Ganesha. Ganesha happily accepts them as offerings. In the Shiva Purana (Śiva Purāṇa), Ganesha cleverly wins the two desirable daughters of Prajāpati by outwitting Karttikeya. Aside from Puranic texts, evidence of Ganesha's links to these goddesses can be found elsewhere. For instance, in the Ganesha Temple at Morgaon (the central shrine for the regional aṣṭavināyaka complex), Buddhi and Siddhi stand to the right and left sides of the Ganesha image. In northern India, the two female figures are said to be Siddhi and Riddhi; Riddhi substitutes for Buddhi with no Puranic basis. These female figures may have originally served as a symbolic suggestion that where Gaṇesha is present, success (siddhi) and wisdom (buddhi) are not far away; the idea that they were actually married to the god probably developed later.
A distinct type of iconographic image of Ganesha depicts him with human-looking females called shaktis, referring to uniquely female creative energy.  These consorts generally lack distinctive personalities or iconographic repertoires. A common depiction of this motif shows Ganesha seated with the shakti upon his left hip. Meanwhile, he turns his trunk to his left to taste the flat cakes or round sweets that the shakti holds in a bowl. In some of the tantric forms of this image, the gesture is modified to take on sexual overtones. According to Ananda Coomaraswamy, the oldest known depiction of Ganesha with a shakti of this type dates from the sixth century C.E.
Whether one is concerned with the successful performance of a religious ceremony, the purchase of a new vehicle, the writing of an examination, the chanting of devotional hymns, or the beginning a business, Ganesha is worshipped. It is widely believed that wherever Ganesha is present, there is success and prosperity. By calling on him, people believe that he will come to their aid and grant them success in whatever endeavors they might be making.
In Hindu temples, Mantras such as Om Gaṃ Ganapataye Namah ("Om, salutation to the Illustrious Ganesha"), are often used to channel Ganesha. Another common form of Ganesha worship is performed by chanting the Ganesha Sahasranamas, which literally means "a thousand names of Ganesha." Each of the god's epithets symbolizes a different aspect of his divine personality, and so by chanting these worshipers are able to contemplate his various benevolent qualities. Offerings are commonly made to Ganesha, in the form of various sweets, such as small sweet balls (laddus). Because of his identification with the color red, he is often worshipped with ruddy objects or substances, such as red sandalwood paste (raktacandana), or red flowers. The worship of Ganesha is considered complementary with the worship of other deities, thus, Hindus of all sects begin prayers, important undertakings, and religious ceremonies with an invocation of Ganesha.
Considering his ubiquitous appeal, worship of Ganesh extends beyond the temple and is carried out in virtually all aspects of life. For example, throughout India and the Hindu diaspora, Ganesha is usually the first icon placed into any new home or abode. As well, Ganesha is particularly adored by dancers and musicians, who begin their performances of arts such as the Bharatnatyam dance with a prayer to him, particularly in South India.
Ganesha is also the focal point of a ten-day festival occurring in the late summer (between late August and mid-September) called Ganesha Chaturthi. On this first day, clay images (murtis) of Ganesha, fashioned by sculptors, are installed in family homes. In this domestic setting, the image is then treated like a kingly guest. On the days and nights that follow, the larger community sets up similar images of Ganesha that serve as the foci for various public performances, including devotional songs, dramas, dances, films, lectures and speeches by public dignitaries. The festival culminates on the day of Ananta Chaturdashi when the images of Ganesha are paraded through the streets and then immersed into water, be it an ocean, river or even a tank, where they quickly dissolve. While this festival is most popular in the state of Maharashtra, it is celebrated by Hindus throughout the whole of India with great devotional fervor. 
Ganesha is a popular figure in Indian art,  and representations of him are not only abundant but also widely varied. He is most consistently and obviously recognizable by way of his elephant head, a feature that has characterized the god since his earliest appearances in Indian art. Ganesha is also commonly depicted with a short, stocky build, and a comfortable pot-belly. It is explained in the Brahmanda Purana that Ganesha has the bulbous paunch due to the fact that all the universes of the past, present, and future exist inside him  The number of Ganesha's arms varies between two and sixteen, though he is most often pictured with four, which is codified as a standard form in some iconographic texts. His earliest images had two arms, and so the presence of only two arms on an image of Ganesha points toward an early origin.  In the typical four-arm configuration, Ganesha's lower right hand holds his broken tusk, a feature which was present even in early depictions. His lower-left hand often holds a bowl of sweet delicacies (modakapātra), which he samples with his trunk, while his upper hands carry an axe and a noose as symbols of his ability to cut through obstacles or to create them as needed. The colors most-often associated with Ganesha are red  and yellow, but other colors are prescribed for use in specific forms and situations. For example, the color white is associated with his representations as Rina-Mochana-Ganapati ("Ganapati Who Releases From Bondage"), while blue is associated with Ekadanta-Ganapati when engaged in meditation. He may be portrayed standing, dancing, taking heroic action against demons, playing with his family as a boy, sitting down, or else engaging in a remarkable range of contemporary activities.
Ganesha is often shown riding on or attended by a small rodent, either a mouse or a rat. In the earliest known images of the god, he is shown without a Vahana (mount), an ommission highly uncharacteristic of most Hindu deities;  by the time of the Puranas however, the mouse as was well-established as Ganesha's mount. The mouse is first mentioned in the Matsya Purana, and later in the Brahmananda Purana as well as the Ganesha Purana  The rodent is also the most common vehicle among Ganesha's avatars. Of the eight incarnations of Ganesha described in the Mudgala Purana, Ganesha has a mouse in five of them, although he uses a lion in his incarnation as Vakratunda, a peacock in his incarnation of Vikata, and a divine serpent in his incarnation as Vighnaraja. In popular iconography of central and western India, says Martin-Dubost, the rodent began to appear as the principal vehicle in sculptures of Gaṇeśa in the seventh century C.E., consistently placed in proximity to the god's feet 
Scholars have wagered many guesses as to what the rodent represents. David Brown suggests that it speaks to Ganesha's status as a god of enterprise, since the rodent rivals the god in his ability to get past any obstacle. A completely different interpretation is given by Krishan, who notes that the rat or the mouse is a destructive creature and a menace to crops. Thus, it was essential to subdue the destructive pest, a type of vighna or impediment to progress that needed to be overcome. By this theory, showing Ganesha as master of the rat proclaimed his function as remover of obstacles, and also suggests his possible role as a village deity who later rose to greater prominence. 
Ganesha has three primary functions: he is 1) the remover or creator of obstacles, 2) the god of Buddhi (or intelligence), and 3) the personification of the primordial sound AUM.
As the "Lord of Obstacles," Ganesha is responsible for creating obstructions of both a material and spiritual order. It is he who places obstacles in the path of those who need to be checked. Thus, Ganesha is thought to be the gatekeeper of shrines, and he is said to corrupt all those who are unworthy of entering such holy places by further deluding their minds with desires.  Ganesha can also remove obstacles for his devotees just as easily. Ganesha's diametrically opposed functions as both obstacle-creator and obstacle-destroyer are vital to his character, giving it significant depth as he is venerable for both negative and a positive reasons.
However, Ganesha does not create or remove obstacles exclusively for the benefit of the righteous. In some cases, he has been known even to place obstacles in the path of the benevolent, as in situations where too many doers of good are going to heaven and thereby crowding the gods. This illustrates Ganesha's ultimate prerogative, which is to uphold the established cosmological hierarchy, whether it be by routing demons, bolstering the authority of the Brahmans, or protecting the interests of the gods. That said, even the gods are not immune from Ganesha's obstacles. In one variation of the famous Hindu myth of the cosmic milk-ocean, the gods churn its waters so singlemindedly that they neglect to pay homage to the supreme Lord Shiva. Although they sought the elixir of immortality, as the end result of their churning, their efforts yield only poison, which begins to spill out of the ocean. The poison spreads upward to the realm of the gods, and so they came to Shiva for refuge, who in turn went to Ganesha. Ganesha informed his father that it was he who had created the obstacle for the purpose of visiting punishment upon the gods for attempting to obtain immortality without Shiva or himself in mind. Thus, no entity in the universe is immune from Ganesha's obstacles.
Ganesha is also considered to be the lord of buddhi, which is a feminine noun that can be variously translated from Sanskrit to English as intelligence, wisdom, or intellect. The concept of buddhi is closely associated with the personality of Ganesha, especially in the Puranic period, where many stories were developed in order to showcase his cleverness and love of intellect. For example, in a late interpolation to the massive epic poem Mahabharata, it is written that the sage Vyasa (Vyāsa) asked Ganesha to serve as his scribe to transcribe the entirety of the poem as he dictated it to him. Ganesha agreed, but only on the condition that, in a truly miraculous exercise of memory, Vyasa recite the poem without interruption. The sage agreed to this condition, and found that in order to obtain occasional reprieve from this exhaustive feat, he needed to recite highly complex passages so that Ganesha would ask for clarifications.
Ganesha is often identified with the Hindu mantra Aum (ॐ, also called Om, Omkara, oṃkāra, or Aumkara), the fundamental sound of the universe. The term oṃkārasvarūpa ("Aum is his form") in connection with Ganesha refers to the belief that he alone is the personification of the primal sound. This association is attested in the Ganapati Atharvashirsa, which describes Ganesha as an incarnation of the sacred sound.
Accordingly, some devotees have even claimed to have seen similarities between the shape of Ganesha's body and the shape of Om in the Devanāgarī and Tamil scripts. With this in mind, numerous ornamentations have been made shaping Ganesha in the calligraphical form of the sacred word.
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