Abstract
In this chapter we present briefly the basic notions of classical and quantum theories of probability and information. This chapter is especially important for biologists, psychologists, experts in cognition, and sociologists who were not trained in quantum theory (but even classical theory is presented in a simple manner). We start with the presentation of the standard measure-theoretic formulation of the modern classical probability theory (Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer, Berlin [1]). Then we turn to fundamentals of quantum formalism, including theory of open quantum systems and its generalizations.
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