Content distributed in a wireless network may be correlated, for example different episodes of a show may have a common background. Exploiting this correlation can potentially enable more efficient content storage in user caches and reduced load for delivery. This talk considers a broadcast caching network with a correlated library. First the two-user, two-file case with arbitrary correlation and an error-free broadcast link is studied. The goal is to characterize the optimal worst case rate-memory function, which is the lowest worst case delivery rate for a given cache size at the users. A two-step cache-aided coded multicast scheme is proposed, in which the first step uses the Gray-Wyner network to represent the library via one common and two private descriptions, and the second step performs cache aided coded multicast by treating these three streams as independent files. Comparing the rate achieved by the proposed two-step scheme with a lower bound derived for correlated files, it is shown that the proposed strategy is optimal for a significant memory regime and it is within half of the conditional entropy of the files for all other memory values. Extensions to larger numbers of files and users, as well as arbitrary demand distributions suggest that exploiting the correlation can result in multiple fold decrease in the expected delivery rate.