The Torah is the Five Books of Moses. It is the holiest of
Jewish books.
The Tanach, which is the Hebrew Bible, contains the Torah, the
Prophets and the Scriptures. Together, these make up the written
law.
The Oral Law was passed down through oral tradition until Rabbi
Judah HaNasi felt (1800 years ago) that it might eventually be
forgotten. He transcribed it; and it is called the Mishna. The
Mishna is expounded upon in the Gemara; and together they make up
the Talmud.