What are the 7 Noachide Laws? And where do we know them from?
The primary codification of the Sheva Mitzvos B'nei Noach, the Seven Noachide Laws, can be found in the Rambam's Mishneh Torah [also known as Yad Chazakah] Hilchos Melachim 9:1 and are elaborated upon in chapters 9 and 10.
According to the Rambam they consist of the prohibition against Avodah Zarah (Idolatry),against cursing G-d, against Murder, against giluy arayos (incest/adultery), theft, eating flesh from a live animal, and the positive command to establish courts.
The source[s] of these mitzvos in Chazal are Sanhedrin 56a and Genesis Rabba 16:6.