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Some useful books available online (see also the syllabus):
  • Michelle Wachs, Poset topology: tools and applications, arXiv:math/0602226.
  • Anders Björner, Topological methods, available at his webpage.
  • Jakob Jonsson, Simplicial complexes of graphs, downloadable from Springer.
  • Dmitry Kozlov, Combinatorial algebraic topology, downloadable from Springer.
  • Jiří Matoušek, Using the Borsuk-Ulam Theorem, downloadable from Springer.
  • Allen Hatcher, Algebraic topology, available at his website.

Wikipedia is, perhaps surprisingly, not a bad source for background material on basic definitions and results in many areas of mathematics, including combinatorics.