History of Computational Group Theory BACKGROUND MATERIALS Fundamentals Group Actions Series Presentation of Groups Presentation of Subgroups Abelian Group Presentations Representation Theory, Modules, Extension, Derivations, and Complements Field Theory REPRESENTING GROUPS ON A COMPUTER Representing Groups on Computers The Use of Random Methods in CGT Some Structural Calculators Computing with Homorphisms COMPUTATION IN FINITE PERMUTATION GROUPS The Calculation of Orbits and Stabilizers Testing for Alt (W) and Sym (W) Finding Block Systems Bases and Strong Generating Sets Homomorphisms from Permutation Groups Backtrack Searches Sylow Subgroups, P-cores, and the Solvable Radical Applications COSET ENUMERATION The Basic Procedure Strategies for Coset Enumeration Presentations of Subgroups Finding All Subgroups Finding All Subgroups Up to a Given Index Applications PRESENTATION OF GIVEN GROUPS Finding a Prese...