Lectures on quantum probability

We introduce the notions of state and observable, the definition of a completely and conditionally completely positive map and explain the relationship between classical and quantum Markov evolution equations. The construction of the minimal solution for the master Markov equation is given, which generalizes to the quantum case the well-known construction of the minimal solution for the Kolmogorov-Feller equation. Introduction Probabilities and mean values in QP Evolution equations Conditional complete positivity Minimal solution of MME Nonexplosion conditions for MME Sufficient nonexplosion conditions Applications to Markov processes Evolution in operator algebras Quantum stochastic processes Quantum stochastic differential equations Symmetric quantum boundary value problem.