Introduction to operator algebras

I will give a quick introduction to operator algebras. Operator algebras in this talk consist of linear operators over some Hilbert space. Their study was initiated by Murray and von Neumann, motivated partially by the mathematical foundation of quantum mechanics. Starting from the definitions of a few basic notions, I will explain that commutative operator algebras can be interpreted as spaces. On the other hand, simple operator algebras (i.e., those without non-trivial ideals) form a class of operator algebras opposite to commutative ones and have attracted many operator algebraists. I will try to introduce several examples of simple operator algebras, some of which appear in mathematical physics. If time permits, I will also give recent results on ideals in C*-algebras. People with any scientific background are welcome.