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Morse theory gives conditions under which analytical information (the critical points of a manifold) translate into topological information (a handle decomposition of the manifold). Cerf theory gives a way to understand the space of all Morse functions on a manifold. This talk will introduce Morse theory, handle decompositions, and Cerf theory for closed manifolds, and end with a generalization to an equivariant model of the same for manifolds with reflection symmetry.