It should be explained that, last summer, Bob Hart and Catalin Rada
started giving a reading course on Operator Algebras, which sort of died.
Here are two sets of notes based on their lectures.
Somebody else's notes on C*-algebras, not
containing proofs: this one does not apply quite as directly, but
does contain some interesting ideas, such as that of a `Functional
Calculus', which might be helpful from a cultural point of view.