Expository reference on group presentations I'm looking for expository papers, small books or chapters on the topic of group presentations. I have familiarity with basic abstract algebra (groups, rings, modules, some finite field theory from number theory...) and some more general, 'categoric' concepts such as free structures, projective structures, exact sequences and functors. My last thoughts were trying to make a connection between extensions of arbitrary groups and extensions of free groups, and that ended up involving group presentations a lot. My knowledge of group presentations was very limited and naive (mostly from conversations with senior students), and I'm looking forward to learn more. Thanks in advance, and any material is welcome. Apart from English, texts in French, Spanish or Portuguese are also accessible to me.

The standard reference for presentations is the book _Combinatorial Group Theory_ by Magnus, Karrass and Solitar.

The word "standard" is subjective.

See also the book _Combinatorial Group Theory_ by Lyndon and Schupp (named in honour of Magnus, Karrass and Solitar). There is also the book _Presentations of groups_ by D.L. Johnson which I grew fond of during my PhD. It is thinner than Magnus, Karrass and Solitar and than Lyndon and Schupp, but has a killer last chapter on cyclically presented groups.