This book presents the basic methods of designing efficient parallel algorithms for graph matching problems. The main goal is to bring together combinatorial, algebraic and probabilistic approaches and to show how this works in the development of efficient parallel algorithms for interesting combinatorial examples of the matching problem. Such a combination of many approaches makes the matching problem an attractive and fascinating subject and a meeting point for many interesting algorithmic techniques as well as new algebraic and geometric areas. Simple representation of many interesting algorithms by means of examples and illustrations has been provided. The authors deserve compliments to have provided in this book a straightforward algorithmic introduction together with a set of example problems specially designed for students.