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...</p>

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

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

**UPDATE**: Follow <a href="https://mathoverflow.net/questions/3858/introductive-text-on-geometric-group-theory">books on geometric-group theory</a> to a more especific titles mentioned here in MO.