Chapter 1 Fundamentals
1.1.Operators and C*-algebras
1.2.Two density theorems
1.3.Ideals, quotients, and representations
1.4.C*-algebras of compact operators
1.5.CCR and GCR algebras
1.6.States and the GNS construction
1.7.The existence of representations
1.8.Order and approximate units
Chapter 2 Multiplicity Theory
2.1.From type Ⅰ to multiplicity-free
2.2.Commutative C*-algebras and normal operators
2.3.An application: type Ⅰ von Neumann algebras
2.4.GCR algebras are type Ⅰ
Chapter 3 Borel Structures
3.1.Polish spaces
3.2.Borel sets and analytic sets
3.3.Borei spaces
3.4.Cross sections
Chapter 4 From Commutative Algebras to GCR Algebras
4.1.The spectrum of a C*-algebra
4.2.Decomposable operator algebras
4.3.Representations of GCR algebras
Bibliography
Index
