The Talmud is an encyclopedia of Jewish cultural tradition that was designed to supplement the Hebrew Old Testament. It evolved over an era from about 450 B.C. to A.D. 500.
The Talmud (from a Hebrew word which means "study") developed in two stages. The oldest was the Mishnah ("to repeat"), a collection of six main segments that dealt with agricultural laws, festivals, family matters, civil/criminal laws, temple laws, and impurities. Later came the Gemara ("learning"), which contained discussions by Jewish rabbis regarding the Mishnah.
The Mishnah, usually referred to as the "oral law," existed in written form by the end of the second century A.D.; the Gemara, the commentary on the law, was formed between A.D. 200 and 500.
When Jesus referred to the "traditions" of the fathers (Matthew 15:1ff; Mark 7:3ff), he was speaking of those human rules (frequently bound by the rabbis as "law") which were later incorporated into the written Talmud.
The Talmud provides scholars with a rich depository of information about Jewish beliefs and practices in the first century.