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Morse theory is a tool for connecting analytical information (the critical points of a manifold) to topological information (a handle decomposition of the manifold) and algebro-topological information (the homology groups of the manifold). This talk will consist of an introduction to Morse theory, followed by an introduction to handle decompositions and homology and a description of how these can be obtained from Morse-theoretic information. Finally, I will describe how these constructions generalize to equivariant descriptions of manifolds with reflection symmetry.