Readers are invited to read a book by the outstanding Russian physicist and physicist-chemist L. S. Polak (1908-2002), which examines the development of variational principles of mechanics, as well as some of their applications in physics, including their role in thermodynamics, field theory, quantum mechanics, etc. The book was the author's doctoral dissertation, published in the form of a monograph, and was appreciated by contemporaries as a fundamental contribution to analytical mechanics, the history of science and theoretical physics in general. The book will be of interest to physicists, mathematicians, historians of science, graduate students and students of relevant specialties.