Statistical Physics of Non Equilibrium Quantum Phenomena This book provides an introduction to topics in non equilibrium quantum statistical physics for both mathematicians and theoretical physicists. The first part introduces a kinetic equation of Kolmogorov type which is needed to describe an isolated atom (actually in experiments an ion) under the effect of a classical pumping electromagnetic field which keeps the atom in its excited state(s) together with the random emission of fluorescence photons which put it back into its ground state. The quantum kinetic theory developed in the second part is an extension of Boltzmanns classical (non quantum) kinetic theory of a dilute gas of quantum bosons. This is the source of many interesting fundamental questions particularly because if the temperature is low enough such a gas is known to have at equilibrium a transition the Bose–Einstein transition where a finite portion of the particles stay in the quantum ground state. An important question considered is how a Bose gas condensate develops in time if its energy is initially low enough Part I Statistical Physics of the Interaction of a Single Atom or Ion with Radiation Introduction The Kolmogorov Equation for a Two Level System The Statistical Theory of Shelving Summary Conclusion and Appendix of Part 1 Part II Statistical Physics of Dilute Bose Gases Introduction Quantum Boltzmann Equations Formation of Singularities Hydrodynamic Approximations Equilibrium Properties of a Dilute Bose Gas with Small Coupling at First Order Mathematical Analysis of the Coupling Condensate Thermal Cloud Systems