Lars Tuset is Professor of Mathematics at Oslo Metropolitan University. He has worked actively in the area of operator algebras and quantum groups since locally compact quantum groups were introduced in the 90’s, and offers firsthand experience of the development of the theory with all its pros and cons. He has previously published a monograph on compact quantum groups and their representation categories. His research includes amenability of locally compact quantum groups, and cocycle deformations of coactions of locally compact quantum groups in the context of crossed products.

• Preface.- Set theoretic preliminaries.- Banach spaces.- Bases in Banach spaces.- Operators on Hilbert spaces.- Spectral theory.- States and  representations.- Types of von Neumann algebras.- Tensor products.- Unbounded operators.- Tomita-Takesaki theory.- Spectra and type III factors.- Quantum groups and  duality.- Special cases.- Classical crossed products.- Crossed  products for quantum groups.- Generalized and continuous crossed products.- Basic construction and quantum groups.- Galois objects and  cocycle deformations.- Doublecrossed  products of quantum groups.- Induction.-Appendix.- Bibliography.- Index.- Exercises.

Lars Tuset is Professor of Mathematics at Oslo Metropolitan University. He has worked actively in the area of operator algebras and quantum groups since locally compact quantum groups were introduced in the 90’s, and offers firsthand experience of the development of the theory with all its pros and cons. He has previously published a monograph on compact quantum groups and their representation categories. His research includes amenability of locally compact quantum groups, and cocycle deformations of coactions of locally compact quantum groups in the context of crossed products.

• Preface.- Set theoretic preliminaries.- Banach spaces.- Bases in Banach spaces.- Operators on Hilbert spaces.- Spectral theory.- States and  representations.- Types of von Neumann algebras.- Tensor products.- Unbounded operators.- Tomita-Takesaki theory.- Spectra and type III factors.- Quantum groups and  duality.- Special cases.- Classical crossed products.- Crossed  products for quantum groups.- Generalized and continuous crossed products.- Basic construction and quantum groups.- Galois objects and  cocycle deformations.- Doublecrossed  products of quantum groups.- Induction.-Appendix.- Bibliography.- Index.- Exercises.