Avot: "Fathers," often used for Abraham, Isaac, and Jacob. Also used for a tractate completed by 200 A.D. of the oral Torah, and for commentaries on that tractate.
Midrash, plural Midrashim: "investigation," refers to 1) the activity of exegesis of the Scriptures, 2) the interpretations that result from that exegesis, 3) the written documents that are a collection of those interpretations.
Mishnah: code of Jewish law, derived from the Pentateuch and passed down by oral tradition. The most famous version of the encoding of the oral Torah was completed around 200 A.D. by Patriarch Judah in Palestine, but there are other versions, notably Mishnah Torah, a commentary on the Mishnah written by Rambam/Maimonides.
Mitzvah, plural Mitzvot: commandment, commandments of the Law. There are 613 mitzvot recorded in Deuteronomy.
Rabbah, Midrash Rabbah: midrash texts on the five books of the Pentateuch and Ruth, Esther, Lamentations, Eccelesiastes, and Song of Songs. Compiled and collected from about the 4th century A.D. through the 9th.
Rambam: initials of Rabbi Moshe ben Maimon (1135-1204, Spain, Morocco, Egypt), aka Maimonides, philosopher and commentator.
Ramban: initials of Rabbi Moshe ben Nahman (1194-1270, Spain), commentator.
Rashi: initials of Rabbi Shelomo Yitzhaki (1040-1105, France), the foremost medieval commentator on the Torah.
Talmud: code of Jewish law, philosophy, and ethics, collected between 200 and 500 A.D. in both Palestine and Babylon.
Tanakh: the Scriptures, comprising the Pentateuch (aka Torah), Prophets, and Writings.
Tanhuma: midrash written as homilies on the Pentateuch.
Torah: "instruction," the Law, the Word of God, also used to designate the Pentateuch. The oral Torah, as written down in the Mishnah, informs the written Torah, as contained in the Pentateuch. Both were handed down by God to Moses at Sinai, and the written Torah must be read in light of the oral Torah. The Torah existed "In the Beginning."
Genesis Rabbah I.i.2Proverbs 8 is speaking of Holy Wisdom, known as Hagia Sophia to Christians, whose person is the Incarnate Word. Read John 1:1-18 in light of the above. For myself, this is an example of the illumination that can be found when reading rabbinical commentaries on the Old Testament.
A. In the beginning God created (Genesis 1:1) [As to the verse, Then I was beside Him like a little child, and I was daily his delight, rejoicing before him always, rejoicing in his inhabited world, and delighting in the sons of men] (Proverbs 8:30-31).
B. The word [for child also may be read to] mean "workman."
C. [In the cited verse] the Torah speaks, "I was the work-plan of the Holy One, blessed be He."
D. In the accepted practice of the world, when a mortal king builds a palace, he does not build it out of his own head, but he follows a work-plan.
E. And [the one who supplies] the work-plan does not build out of his own head, but he has designs and diagrams, so as to know how to situate the rooms and the doorways.
F. Thus the Holy One, blessed be He, consulted the Torah when He created the world.
G. So the Torah stated, By means of "the beginning" [that is to say, the Torah] did God create (Genesis 1:1).
H. For the word the beginning refers only to the Torah, as Scripture says, The Lord made me as the beginning of his way (Proverbs 8:22).
Warning: I am not a Jewish scholar, nor have I read enough works to think that I have an intuitive grasp on Jewish interpretation. I do, however, often find it insightful, while trying to play close attention to not distort the words of the rabbis to something unfaithful to the text, as I extend the writings to Christianity (in other words, I try to avoid proof-texting, and will read an entire rabbah, its sources, and other commentaries such as Rashi's, before developing my thoughts on a particular part). I will mostly be using Jacob Neusner's translations of Hebrew and Aramaic texts, while largely ignoring his controversial interpretations.
Please feel free to correct me, disagree, or provide additional texts in the comments.