Sander Zwegers defined indefinite theta functions to give a uniform construction and generalization of Ramanujan's "mock theta functions," originally a finite list of q-series satisfying some remarkable identities. I will define indefinite theta functions, harmonic weak Maass forms, and mock modular forms, and explain how they are related. Time permitting, I will discuss some of my own research on Mellin transforms of indefinite theta functions. Speaker(s): Gene Kopp (UM)