Textbook in PDF format GAP stands for Groups, Algorithms and Programming. The name was chosen to reflect the original aim of the system, which is introduced in this reference manual. Since that choice, the system has become somewhat broader, and you will also find information about algorithms and programming for other algebraic structures, such as semigroups and algebras. This manual, the GAP Reference Manual contains the official definitions of GAP functions. It should contain all the information needed to use GAP, and is not intended to be read cover-to-cover. This is one of the manuals documenting the core part of GAP, the others being the GAP Tutorial and HPC-GAP Reference Manual. There is also a document CHANGES.md on the changes from earlier versions in the root directory. This preface serves not only to introduce “The GAP Reference Manual”, but also as an introduction to the whole system