Knuth's multivolume analysis of algorithms is widely recognised as the definitive description of classical computer science. The first three volumes of this work have long comprised a unique and invaluable resource in programming theory and practice. Scientists have marvelled at the beauty and elegance of Knuth's analysis, while practicing programmers have successfully applied his "cookbook" solutions to their day-to-day problems. The book is Volume 4A, because Volume 4 has itself become a multivolume undertaking. Combinatorial searching is a rich and important topic, and Knuth has too much to say about it that is new, interesting, and useful to fit into a single volume, or two, or maybe even three. This book alone includes approximately 1500 exercises, with answers for self-study, plus hundreds of useful facts that cannot be found in any other publication. Volume 4A surely belongs beside the first three volumes of this classic work in every serious programmer's library.