  These notes are intended as an introduction to a study of applications of
noncommutative calculus to quantum statistical Physics. Centered on
noncommutative calculus we describe the physical concepts and mathematical
structures appearing in the analysis of large quantum systems, and their
consequences. These include the emergence of algebraic approach and the
necessity of employment of infinite dimensional structures. As an illustration,
a quantization of stochastic processes, new formalism for statistical
mechanics, quantum field theory and quantum correlations are discussed.
