In mathematics, factorization represents the decomposition of an object (e.g. a number, a polynomial, or a matrix) into a product of other objects, called factors. However, in the case of more complex algebraic objects, it may not be clear what the factors or basic building blocks are. In this book, by factorization of a group we assume representation of a group as the direct product of its subsets. Group factorization is a topic that besides its theoretical beauty has practical uses in graph theory, coding theory and cryptography. The book contains many relevant, but well known results, extended by a set of new results, with emphasis on the factorization of nonabelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. This book can be useful for a reader, familiar with basic concepts of algebra, interested not only in the foundation of the topic, but for anyone who has already research interest in the group factorizations. Researchers will find generalization of some known results and even material that has not yet been published.

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