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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.

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    $\begingroup$ See the references here. $\endgroup$
    – Dietrich Burde
    Commented Apr 1, 2016 at 15:58

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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.

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  • $\begingroup$ Your answer and Rotman's review of Johnson's book are inclining me to go after it first. Also, my local university's library has a copy of Magnus' book. I guess I'll go for Johnson's first, and use Magnus' as a second reference. $\endgroup$
    – Henrique Augusto Souza
    Commented Apr 1, 2016 at 16:10

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