Mosaism is the religious system present in the Tanach (specifically the Torah), or Old Testament of the Christian Bible. It is built on the revealed word of God to His servant Moses at Mount Sinai, and in the years following. It consists of purity laws and rites of status, but most importantly it describes the righteous way for the people of God to behave, and the system of sacrifices established to maintain a right relationship between the people and their God when the people fail to live up to the expectations of God.
NOTE: This is the primary difference between ancient Jewish practice and current, that is, the necessity of sacrifice to atone for sins. Mosaic law reflects that man has fallen short of the will of God, and because God is the source of life, separation from Him (sin) can only be rectified through death, mercifully allowed to be representative. A sacrifice was more than just the death of an animal, it was akin to giving something very important and close to ones heart as recompense for mercy and restored relationship, an apology really.