"The Talmud has two components: the Mishnah (Hebrew: משנה, c. 200 CE), the first written compendium of Judaism's Oral Law, and the Gemara (c. 500 CE), an elucidation of the Mishnah and related Tannaitic writings that often ventures onto other subjects and expounds broadly on the Hebrew Bible." -Wikipedia
So, long story short:
Talmud (means instruction) is the second important text after the Torah. It is the rabbinical writings. It has two parts: First, Mishnah, the earliest collection of those writings, laws based on Torah but not of the Torah. Second, Gemara, explanation of Mishnah and other stuff. The production of Talmud was chiefly in Babylon (where some Jews remained after the Babylonian captivity), after the destruction of Jerusalem by the Romans.
Targum (means Explanation) is basically commentaries of Torah.