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Every compact orientable 3-manifold can be broken into two simple pieces, called a Heegaard splitting. There is a notion of stabilization on these splittings, and in fact any two such splittings are identical after enough stabilizations. This is called the Reidemeister-Singer theorem. I will describe Heegaard splittings and prove that they always exist. I will give some simple examples of the decompositions. If there is time, I will provide some intuition as to why a 3-manifold can have multiple Heegaard splittings of a given complexity.