1 Quantum Boltzmann Statistics in Interacting Systems -- 1 Introduction -- 2 Quantum Boltzmann statistics for entangled operators -- 3 References -- 2 Interaction Representation Method for Markov Master Equations in Quantum Optics -- 1 Sufficient conditions for conservativity -- 2 A priori bounds -- 3 Structure of generators of MME in quantum optics -- 4 Examples -- 5 Discussion -- 6 References -- 3 A Stochastic Variational Principle for Burgers Equation and its Symmetries -- 1 Introduction -- 2 Variational problem -- 3 Stochastic first integrals -- 4 An integration by parts formula -- 5 References -- 4 Noncommutative Versions of Prohorov and Varadhan Theorems -- 1 Vague and narrow convergence of positive functionals -- 2 Noncommutative large deviations -- 3 References -- 5 Gaussian Domination and Bose-Einstein Condensation -- 1 Introduction -- 2 Some Historical Remarks -- 3 Model Systems -- 4 Gaussian Domination and its Application to the Study of Bose Systems -- 5 References -- 6 Quantum Markov Semigroups and their Stationary States -- 1 Introduction -- 2 Ergodic theorems -- 3 The minimal quantum dynamical semigroup -- 4 The existence of Stationary States -- 5 Faithful Stationary States and Irreducibility -- 6 The convergence towards the equilibrium -- 7 References -- 7 Exponential Decay for Perturbations of Pure Point Hamiltonians -- 1 Introduction -- 2 Absolutely continuous perburbations of pure point operators -- 3 Sojourn time and Spectral Entropy -- 4 References -- 8 Propagation of Chaos in Classical and Quantum Kinetics -- 1 Overview -- 2 Classical and Quantum Molecular Chaos -- 3 Classical Manifestations of the Propagation of Quantum Molecular Chaos -- 4 Acknowledgements -- 5 References -- 9 Imprimitivity Systems and Quantum Codes -- 1 Introduction -- 2 Imprimitivity systems and quantization of classical codes -- 3 Tensor products of imprimitivity system and quantum codes -- 4 References -- 10 Boson Fock Algebra on the Unit Ball of the d-Dimensional Complex Numbers -- 1 Introduction -- 2 Operators on the algebra A0 (Bd) -- 3 Introduction to Boson Fock space -- 4 Boson Fock space on the unit ball -- 5 References.