Abstract: This is going to be a chapter of a volume entitled ``Geometric Combinatorics'' in the IAS/Park City Mathematics series. It is based on a series of lectures that I gave at the graduate school of the IAS/Park City Mathematics Institute in 2004. The goal of these lecture notes is to provide students with the skills to do research in the area of poset topology. It contains introductory material as well as recent developments and open problems.
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