The book is devoted to the foundations of quantum mechanics and those questions in which probabilistic and statistical representations play a significant role. Progress has been made in the field in recent years, spurred largely by new applications of quantum theory in computer science. The book discusses in an accessible and mathematically rigorous form issues of probabilistic interpretation, quantum mechanical symmetries, the problem of correspondence between classical and quantum observables (observed "time," "phase," "angle"), the theory of canonical commutation relations and Gaussian states, non-standard uncertainty relations ("time - energy," "phase - number of quanta," "angle - angular momentum"), Rao quantum inequalities - Cramer and other fundamental boundaries of quantum measurement accuracy.