There is a [book][1]  devoted entirely to KKM theory and its applications. It contains
an outline of the classical KKM theorem as well as a number of generalizations. Another standard reference is ["Fixed point theory"][2] by Granas and Dugundji.

  [1]: http://books.google.co.uk/books?id=h_DaTNA8mw8C&printsec=frontcover&dq=kkm+theory&hl=en&ei=zm5ITJvNN8n24ga9yZneDA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCwQ6AEwAA#v=onepage&q&f=false
  [2]: http://books.google.co.uk/books?id=4_iJAoLSq3cC&printsec=frontcover&dq=dugundji+fixed+points&source=bl&ots=2lOqh3YAne&sig=JdRiTZFR0yHSEoWT8N4jjOZqQAo&hl=en&ei=VGxITLn9E4vNjAeg0PnUDg&sa=X&oi=book_result&ct=result&resnum=3&ved=0CB8Q6AEwAg#v=onepage&q=dugundji%2520fixed%2520points&f=false