Some core beliefs of Judaism include the belief in God as the one and only God, that the Torah is the most important Jewish text, and that God established a covenant with Abraham to be passed on to future generations. Judaism believes that the God gave the Torah and the oral Torah to Moses and that his prophesies must be true.
In the "Thirteen Principles of the Faith," written by influential rabbi Moshe ben Maimon in the 12th century, the first five principals relate to the belief in one God. These principals state that God created all things, that God is alone in his oneness and that believers must not pray to any other gods or things.
Circumcision is part of the covenant with God, which passes on the covenant to the new generation. Jews also generally believe that anyone who's mother was Jewish is themselves Jewish, even if they no longer follow the religion. Outsides may convert to Judaism, but it is a complicated process.
More controversial beliefs within Judaism include the belief in the future coming of the Messiah and that God will bring the dead back to life. Many conservative and reform Jews do not accept these principals, despite being included in the oft cited "Thirteen Principals of Faith."