Hodge theory is an invaluable tool for not only analytic/differential geometers, but also those algebraic geometers interested in schemes over the complex numbers. We will recall some general Hodge theory and some of the ways in which Hodge theory relates to algebraic geometry over C (and over more!). Depending on the time left, we will then see how these Hodge-theoretic tools crucially show up in the study of deformations of varieties.