Torah: The five books of Moses (Genesis, Exodus, Leviticus, Numbers, Deuteronomy)
Documentary Hypothesis (18th-Century theory, but still in dispute):
               Based on discussion by W. Gunther Plaut in The Torah: A Modern Commentary

• "J" thread: Jahwist (uses YHVH): most of Genesis
• "E" thread: Elohist (uses Elohim): some scenes of Genesis, including the binding of Isaac,
  most of Exodus and Numbers
• "D" thread: Deuteronomist (Deuteronomy)
• "P" thread: Priestly (Leviticus, 1st chapter of Genesis, passages concerned with genealogies
  and priesthood; latest written, during or after Babylonian exile)

Tanakh: Torah, plus Nevi'im (Prophets) and Kethuvim (Writings)
Roughly equivalent to the Christian Old Testament, but in a different order

Oral Law: The interpretation and commentary on the Torah
Rabbi Telushkin's 3 reasons the Oral Law is necessary (from Jewish Literacy):

1. The frequent lack of detail in Torah legislation
2. The incomprehensibility of some terms in the Torah
3. The objections to following some Torah laws literally.

Mishna: Systematic written codification of Oral Law by Rabbi Judah the Prince, in about 200 C.E.
-- 6 "orders" with a total of 63 tractates, including the Pirkei Avot

The Orders:

• Zera'im (Seeds)
• Mo'ed (Holidays, including Shabbat observance)
• Nezikin (Damages)
• Nashim (Women)
• Kodashim (Sacrifices and Ritual Slaughter)
• Taharot (Laws of Purity and Impurity)

Gemara: Written record of Rabbinic discussion of Mishna

Talmud: Combination of Mishna and Gemara

• Palestinian or Jerusalem Talmud (about 400 C.E.)
• Babylonian Talmud (about 500 C.E.)