This book mainly introduces some recent applications of the theory of semi-tensor product of matrices. In particular， we put emphasis on the applications in the fields of fuzzy logical systems， finite state machines and graphs. In the area of the fuzzy logical systems， we limit our discussions to the method of solving the fuzzy logical equation， which is a key technology in the analysis and synthesis of the logical dynamical systems. On the side of the applications in the finite state machines， we present the advances on the mathematical formulation， compatible analysis， reduction and language recognition. In the field of graph theory， we focus on the structure analysis and its applications.This book is not only suitable for professional researchers in the fields of control science and engineering， industrial automation， electrical automation and mechanical engineering， but also can be used as a reference material for relevant scientific and technical engineers.