There is given the complete exposition of a mathematical formalism and the working tools of mechanics of multibody systems based on methodology of the system analysis. Essentially in a new fashion the problem of designing of the differential equations of constraints of a general kind of multibody systems with environment bodies is represented. Two algorithms of direct analytical designing of a reverse matrix of kinetic energy of system are developed, passing stages of designing of the matrix and its subsequent reversing. The created algorithms are most numerically economic among known. Although this is complex material, the book is built on transparent relatively simple principles, and readers with less experience in the field of mechanics will find enough material to give them a good introduction in the points under consideration. Audience: Graduate students and researchers in the field of mechanics and control. The prerequisite for reading this book is roughly the mathematical sophistication acquired in a typical undergraduate mathematics education.