Invariant Means and Finite Representation Theory of C^{*}-Algebras.

Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. Notation, definitions and useful facts -- Chapter 3. Amenable traces and stronger approximation properties -- 3.1. Characterizations of amenable traces -- 3.2. Uniform amenable traces -- 3.3. Quasidiagonal traces -- 3.4. Locally finite dimensional traces -- 3.5. Miscellaneous remarks and permanence properties -- Chapter 4. Examples and special cases -- 4.1. Discrete groups -- 4.2. Nuclear and WEP C*- algebras -- 4.3. Locally reflexive, exact and quasidiagonal C*-algebras -- 4.4. Type I C*-algebras -- 4.5. Tracially AF C*-algebras -- Chapter 5. Finite representations -- 5.1. Ili-factor representations of some universal C*-algebras -- 5.2. Elliott's intertwining argument for IIi-factors -- 5.3. Hi-factor representations of Popa Algebras -- Chapter 6. Applications and connections with other areas -- 6.1. Elliott's classification program -- 6.2. Counterexamples to questions of Lin and Popa -- 6.3. Connes' embedding problem -- 6.4. Amenable traces and numerical analysis -- 6.5. Amenable traces and obstructions in K-homology -- 6.6. Stable finiteness versus quasidiagonality -- 6.7. Questions -- Bibliography.

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