This is a specialized textbook on graph factorizations, an area which lies partly in graph theory and partly in the theory of combinational designs. It is the first full-size book on its particular subject, which has previously been treated only in survey papers and in chapters in books on design theory and on graph decompositions and matching theory. The book is intended for beginning graduate students in Combinatorial Mathematics, and may be used as a text for a special topics course; but it reaches to the boundaries of current research and will also prove useful as a reference source for professionals in the field. It contains a number of easy exercises, together with some which are challenging, and a few unsolved problems. There is an extensive bibliography.