The source of the 613 commandments is the Torah, which is comprised of the first five (5) books of the Hebrew Bible: Genesis, Exodus, Leviticus, Numbers, and Deuteronomy.

The great Jewish sage, Maimonides, in his book, Sefer Hamitzvot, provides a list of all of the 613 commandments and where they are located in the Torah. You can find his list of the 613 commandments and where in the Torah they were found here:

[link to en.wikipedia.org (secure)]

After the great Flood, the covenant between the Creator, Noah, and Noah's descendants is briefly mentioned in Genesis 9. Here is the list of Noahide laws, and where in scripture you can learn more about these rules:

Not to worship idols - Ex. 20:3. Lev. 24:16
Not to curse G-d - Ex. 22:27, Lev. 24:10-17
Establish laws and courts of justice - Gen. 9:5-6
Not to commit murder - Gen. 9:6. Ex.: 24:3
Not to commit forbidden sexual relations - Gen. 2:24, 20:13, 19:29-36
Not to steal - Gen. 2:16-17, 34:2
Flesh of a living animal prohibited - Genesis 9:4

The Noahide laws are the basic laws for civilization. The 613 laws are designed for the Jewish people to follow.