This book is based on a lecture course delivered by the authors over a period of many years to the students in mechanics at the St. Petersburg State Technical University (the former Leningrad Polytechnic Institute). The material differs from numerous traditional text books on Theory of Machines and Mechanisms through a more profound elaboration of the methods of structural, geometric, kinematic and dynamic analysis of mechanisms and machines, consisting in both the development of well-known methods and the creation of new ones that take into account the needs of modem machine building and the potential of modem computers. The structural analysis of mechanisms is based on a new definition of structural group which makes it possible to consider closed structures that cannot be reduced to linkages of Assur groups. The methods of geometric analysis are adapted to the analysis of planar and spatial mechanisms with closed structure and several degrees of movability. Considerable attention is devoted to the problems of con figuration multiplicity of a mechanism with given input coordinates as well as to the problems of distinguishing and removing singular positions, which is of great importance for the design of robot systems. These problems are also reflected in the description of the methods of kinematic analysis employed for the investi gation of both open ("tree"-type) structures and closed mechanisms.