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Kac-Moody Lie algebras are infinite-dimensional Lie algebras whose theory is remarkably similar to finite-dimensional semisimple Lie algebras. Affine Lie algebras are the most important special case.We will develop some of the Kac-Moody theory, such as the Kac-Weyl character formula, before specializing to affine Lie algebras. Ideas from physics give a multiplication called fusion on the irreducible integrable representations of fixed level. Kac and Peterson showed that the characters and related "string functions" of these representations are modular forms, and the transformation properties of these theta functions of fixed level encode important information about the fusion ring. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc. May be repeated for credit.