This book is a translation of the first volume of the two-volume "Lee Group Theory" K. Chevalle and devoted to the foundations of this theory. The Book of D. Chevalle is a systematic consideration of Lie groups as a whole, as opposed to the local point of view usually held in older manuals. For the first time, this presentation system was implemented by L. C. Pontryagin in his book The Theory of Continuous Groups (G.) T. T. and . 1938), in which, however, the theories of the Lie groups themselves are devoted only to the last chapters. Book K. Chevalle is designed for academics, undergraduates and graduate students. For its reading, it is necessary to possess the basic concepts of combinatorial and set-theoretic topology and abstract group theory.