  Mock modular forms have their origins in Ramanujan's pioneering work on mock
theta functions. In a 1975 paper, Zagier proved certain transformation
properties of the generating function of the Hurwitz class numbers $H(n)$ for
the discriminant $(-n)$. In the modern framework, these results show that the
generating function of $H(n)$ is a mock modular form of weight 3/2 with the
theta function being the shadow. In this expository paper, we provide a
detailed proof of Zagier's result.
