For some practical applications, mechanisms are sophisticatedly designed with changeable topologies in order to perform the elaborate tasks. Such mechanisms are called the mechanisms with variable topologies (MVTs). In the past decades, the single-topology mechanisms had been explored exhaustively; however, there are no obvious works which exclusively contribute to the structural characteristics of MVTs. This book is, therefore, devoted to the topology and configuration analysis of mechanisms with variable topologies. First, the current research background of MVTs is reviewed. Then, the topological variability of kinematic joints and mechanisms is introduced. The representation and identification of topological and motion characteristics of MVTs are further provided. Finally, the mobility and special configurations verified by the MVTs are discussed. The material provides a fundamental introduction to the variable-topology mechanisms and addresses some particular properties to this special mechanism. It is suitable to be used as a reference book for the courses of mechanisms and its related as well as for the advance studies in mechanism and machine science.