A primer on computational group homology and cohomology using GAP and SAGE∗

These are expanded lecture notes of a series of expository talks surveying ba-sic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomol-ogy. You should know the definition of a (left) module over a (non-commutative) ring, what Z[G] is (where G is a group written multiplicatively and Z denotes the integers), and some ring theory and group theory. However, an attempt has been made to (a) keep the presentation as simple as possible, (b) either provide an explicit reference or proof of everything. Several computer algebra packages are used to illustrate the computations, though for various reasons we have focused on the free, open source packages, such as GAP [Gap] and SAGE [St] (which includes GAP). In particular, Graham Ellis generously allowed extensive use of his HAP [E1] documentation (which is sometimes copied almost verbatim) in the presentation below. Some interesting work not included in this (incomplete) survey is (for example) that of Marcu