C*-代数的理论和应用涉及算子理论、群表示、拓扑、量子力学、非交换几何等不同领域。林华新著的《顺从C*-代数的分类导引（英文版）》主要介绍了顺从C*-代数的分类及其相关知识，利用K理论对C*-代数进行分类，并对相关问题的研究不断加深。本书适合高年级本科生、研究生，以及数学爱好者参考阅读。
本书的目的是向读者介绍顺从C-代数的分类理论的新进展，读者可以是非专家类读者，也可以是研究生。本书是国内少有的关于C-代数方面的专著，但对于普通读者来讲，阅读还是有难度的。

Preface
Chapter 1 The Basics of C*-algebras
1.1 Banach algebras
1.2 C*-algebras
1.3 Commutative C*-algebras
1.4 Positive cones
1.5 Approximate identities, hereditary C*-subalgebras and quotients
1.6 Positive linear functionals and a Gelfand-Naimark theorem
1.7 Von Neumann algebras
1.8 Enveloping von Neumann algebras and the spectral theorem
1.9 Examples of C*-algebras
1.10 Inductive limits of C*-algebras
1.11 Exercises
1.12 Addenda
Chapter 2 Amenable C*-algebras and K-theory
2.1 Completely positive linear maps and the StLnespring representation
2.2 Examples of completely positive linear maps
2.3 Amenable C*-algebras
2.4 K-theory
2.5 Perturbations
2.6 Examples of K-groups
2.7 K-theory of inductive limits of C*-algebras
2.8 Exercises
2.9 Addenda
Chapter 3 AFoalgebras and Ranks of C*-algebras
3.1 C*-algebras of stable rank one and their K-theory
3.2 C*-algebras of lower rank
3.3 Order structure of K-theory
3.4 AF-algebras
3.5 Simple C*-algebras
3.6 Tracial topological rank
3.7 Simple C*-algebras with TR(A) (_ 1
3.8 Exercises
3.9 Addenda
Chapter 4 Classification of Simple AT-algebras
4.1 Some basics about AT-algebras
4.2 Unitary groups of C*-algebras with real rank zero
4.3 Simple AT-algebras with real rank zero
4.4 Unitaries in simple C*-algebra with RR(A) = 0
4.5 A uniqueness theorem
4.6 Classification of simple AT-algebras
4.7 Invariants of simple AT-algebras
4.8 Exercises
4.9 Addenda
Chapter 5 C*-algebra Extensions
5.1 Multiplier algebras
5.2 Extensions of C*-algebras
5.3 Completely positive maps to Mn(C)
5.4 Amenable completely positive maps
5.5 Absorbing extensions
5.6 A stable uniqueness theorem
5.7 K-theory and the universal coefficient theorem
5.8 Characterization of KK-theory and a universal multi-coefficient theorem
5.9 Approximately trivial extensions
5.10 Exercises
Chapter 6 Classification of Simple Amenable C*-algebras
6.1 An existence theorem
6.2 Simple AH-Mgebras
6.3 The classification theorems
6.4 Invariants and some isomorphism theorems
Bibliography
Index
编辑手记