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**.