There are four versions of Kaddish, which we will identify by name. 1) Half-Kaddish corresponds to the main section of Kaddish. It is called Half-Kaddish to distinguish it from the other Kaddishim which contain further additions. In any part of prayer in which Kaddish must be said, but there should not be prolonged interruption, Half-Kaddish is recited; 2) Kaddish Shalem (Full-Kaddish or Kaddish Yehei Shelama) is recited after saying verses from Tanakh and contains an added request for peace and good life for us and all Israel. It concludes: “Oseh shalom bi-mromav, Hu (be-raĥamav) ya’aseh shalom aleinu ve-al kol (amo) Yisrael ve-imru: Amen” (“May He Who makes peace in His high places make peace (in His mercy) for us and all of (His nation) Israel – and say: Amen”). Since this Kaddish is usually recited by mourners, it is also called Kaddish Yatom (Mourner’s Kaddish); 3) Kaddish Titkabel is recited by the ĥazan after the conclusion of the Amida. It is identical to Kaddish Shalem but for a single additional line that asks for our prayers be accepted; 4) Kaddish De-rabanan is recited after the study of rabbinic teachings. It too is identical to Kaddish Shalem but with the addition of a prayer that those who study Torah be granted long, good lives.
The Sages ordained the recitation of Kaddish at the conclusion of each section of communal prayer. Kaddish De-rabanan is recited after Korbanot,; Half-Kaddish after Pesukei De-zimra; Half-Kaddish after Taĥanun; On Mondays and Thursdays, an additional Half-Kaddish is recited after Torah reading; Kaddish Titkabal is recited after Kedusha De-sidra; Kaddish Shalem is recited after Shir shel Yom; and Kaddish De-rabanan is recited after Pitum Ha-ketoret (Shibolei Ha-leket §8). The recitation of Kaddish concludes and elevates each section of the prayer service toward the ultimate objective – God’s honor – so that we may begin the next section.
The general practice is that mourners recite Kaddish Shalem after the recitation of verses from Tanakh and Kaddish De-rabanan after studying rabbinic works, since the departed souls benefits from Kaddish recited for the purpose of its elevation (see below, sections 18-19). When no mourner is present, one who lost a parent recites the Kaddish. If nobody present has lost a parent, the common custom is to refrain from reciting those Kaddishim (Peninei Halakha: Prayer, 23:8 n. 9).