Sources

Here are the sources I'm using so far; where possible I will try to post links to the pdf files for some of the articles. For others, I'll post links to their Journals' websites. I won't be using all the materials from the sources below .... just what I need as when when I need it.

General Introduction to (Coxeter) Groups

• Combinatorics of Coxeter Groups, Anders Bjorner & Francesco Brenti (2000)
  
• Reflection Groups and Coxeter Groups, James E. Humphreys (1990)
• Introduction to Coxeter Groups, Robert B. Howlett

Infinite Groups, Automatic Groups, Regular Languages, Automata etc.

• GROUPS , GRAPHS & TREES : An Introduction to the Geometry of Infinite Groups, John Meier (2007)
• Word Processing in Groups, David B. A. Epstein, J. W. Cannon, D. F. Holt, S. V.F Levy, M.S. Paterson, W.P. Thurston (1992)
• The Use of Knuth-Bendix methods to solve the word problem in Automatic groups, Journal of Symbolic Computation D. B. A. Epstein, D. F. Holt, S. E. Rees (1991) (available on request)
  
• The Warwick Automatic Groups Software , D. F. Holt (1994)

I don't know what category the rest of my sources fall in. They do however play significant roles in giving me material for the thesis.

• Regular Polytopes, H.S.M. Coxeter (1973)
• Cells in Coxeter Groups , Paul E. Gunnels
  
• The Cayley Graphs of Coxeter and Artin Groups , Carl Droms and Herman Servatius (1993)
• A Transducer Approach to Coxeter Groups , Fokko du Cloux (1999)
• Computation in Coxeter Groups , Bill Casselman (2001ish)

If I was doing this in graduate school ... I would probably be using this book. I have it in my possession but I doubt I will actually get around to using it:

• The Geometry and Topology of Coxeter Groups , Michael Davis (2007)