This book gives a detailed and systematic exposition of the fundamentals of non-relativistic quantum mechanics for those who are not acquainted with the subject. The character of the physics of microparticles and the problems of the physics of microphenomena (interference of amplitudes, the principle of superposition, the specific nature of measuring processes, causality in quantum mechanics) are considered on the basis of concepts about probability amplitudes. Besides, the quantum-mechanical systems - microparticles - with two basic states are analyzed in detail. The apparatus of quantum mechanics is considered as a synthesis of concepts about physics and the theory of linear operators.  A number of specially worked out problems and examples have been included in order to demonstrate the working of the apparatus.This is a completely electronic version typeset in LaTeX from the scanned original.Source files can be found at https://gitlab.com/mirtitles/tarasov-qm