This is the first of several talks introducing the field of C-star algebras to the budding set-theorist. The long-term intent of the talks is to provide enough background on operator algebras for the listener to understand some of the recent developments connecting the two subjects. No experience with operator algebra is required; only the standard undergraduate algebra and analysis. Similarly, any concepts in set theory beyond a first course in the subject will be discussed before being used.

The first 1+epsilon talks will be entirely on C-star algebras. I will start with the definitions and fundamental examples (C(X), algebras of operators), and proceed to some of the basic tools of the theory, namely the continuous functional calculus, and the GNS representation. These results should give a rough idea of the structure of C-star algebras, as well as provide a jumping off point for some of the problems that set theory has some connections to.