For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Volume 2.- States in Quantum Statistical Mechanics.- 5.1. Introduction.- 5.2. Continuous Quantum Systems. I.- 5.3. KMS-States.- 5.4. Stability and Equilibrium.- Models of Quantum Statistical Mechanics.- 6.1. Introduction.- 6.2 Quantum Spin Systems.- 6.3. Continuous Quantum Systems. II.- 6.4. Conclusion.- References.- Books and Monographs.- Articles.- List of Symbols.