This book chronicles the development of graph factors and factorizations. It pursues a comprehensive approach, addressing most of the important results from hundreds of findings over the last century. One of the main themes is the observation that many theorems can be proved using only a few standard proof techniques. This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. In addition to covering the history and development of this area, the book offers conjectures and discusses open problems. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization.

1 Basic Terminology.- 2 Matchings and 1-Factors.- 3 Regular Factors and f-Factors.- 4 (g, f)-Factors and [a, b]-Factors.- 5 [a, b]-Factorizations.- 6 Parity Factors.- 7 Component Factors.- 8 Spanning Trees.