Chapter 1. Basic theory of Hilbert C*-modules 1.1 Hilbert C^*-modules and bounded module mappings 1.2 Polar decomposition and Wold decomposition 1.3 Tensor products of Hilbert C*-modules 1.4 KSGNS construction Chapter 2. Kasprove's stabilization and Fredholm generalized index theory 2.1 Kasprove's stabilization theorem 2.

2 Morita equivalence and C*-correspondence 2.3 Generalized index theory of Fredholm module operators 2.4 Introduction to module frames theory Chapter 3. Quantum Markov semigroups and operator-valued Dirichlet forms 3.1 Module operator semigroups 3.2 Abstract Cauchy problems based on Hilbert A-modules 3.3 Quantum Stone theorem and its application 3.4 Operator-valued Dirichlet forms and quantum Markov semigroups 3.

5 Application in operator-valued free probability.