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Books on geometric group theory, nowaday are talking and applying algebra and topology technologies to algorithms, solvability of word problems, membership problems, context free languages, etc...

All these together with the notes of Peter May refered above, will almost show you the state-of-the-art.

Further, check Graham NIblo work at http://www.personal.soton.ac.uk/gan/Welcome.html

UPDATE: Follow books on geometric-group theory to a more especific titles mentioned here in MO.

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Books on geometric group theory, nowaday are talking and applying algebra and topology technologies to algorithms, solvability of word problems, membership problems, context free languages, etc...

All these together with the notes of Peter May refered above, will almost show you the state-of-the-art.

Further, check Graham NIblo work at http://www.personal.soton.ac.uk/gan/Welcome.html

UPDATE: Follow books on geometric-group theory to a more especific titles here in MO.

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Books on geometric group theory, nowaday are talking and applying algebra and topology technologies to algorithms, solvability of word problems, membership problems, context free languages, etc...

All these together with the notes of Peter May refered above, will almost show you the state-of-the-art.

Further, check Graham NIblo work at http://www.personal.soton.ac.uk/gan/Welcome.html