This book is a thorough and systematic exposition of the foundations of non-relativistic quantum mechanics and is designed for a first-time study of the subject. The first chapter is an introduction to quantum mechanics through analysis of the specific character of microscopic physics. In the second chapter, based upon the concept of amplitude probability, various questions on physics of microphenomena are considered (interference of amplitudes, superposition principle, specificity of measuring act, causality in quantum mechanics). The simplest quantum mechanical systems — microobjects with two basic states are analyzed in detail. In the third chapter we take a look at quantum mechanical methods as a synthesis of physical ideas and the theory of linear operators. Some specially selected examples and problems are presented to demonstrate the application of these methods. This book is intended for students of technical and pedagogical universities, and can also be used by engineers of different specialties.