We first describe some states representing pairs of electrons, and in particular, the singlet state, which is the simplest quantum system that displays entanglement.
We then define a new class of operators, called projection operators, which allows us to calculate averages in a new way.
The third section covers the violation of Bell's Theorem in quantum mechanics. We first describe the classical version, and then show, quantitatively, that it doesn't hold for pairs of electrons in the singlet state.
Finally, we discuss another fundamental result of quantum mechanics, called the No-Cloning Theorem.