In many real world networks agents are initially unsure of each other's qualities and must learn about each other over time via repeated interactions. This paper is the first to provide a methodology for studying the dynamics of such networks, taking into account that agents differ from each other, that they begin with incomplete information, and that they must learn through past experiences which connections/links to form and which to break. The network dynamics in our model vary drastically from the dynamics in models of complete information. With incomplete information and learning, agents who provide high benefits will develop high reputations and remain in the network, while agents who provide low benefits will drop in reputation and become ostracized. We show, among many other things, that the information to which agents have access and the speed at which they learn and act can have a tremendous impact on the resulting network dynamics. Using our model, we can also compute the ex ante social welfare given an arbitrary initial network, which allows us to characterize the socially optimal network structures for different sets of agents. Importantly, we show through examples that the optimal network structure depends sharply on both the initial beliefs of the agents, as well as the rate of learning by the agents. Due to the potential negative consequences of ostracism, it may be necessary to place agents with lower initial reputations at less central positions within the network.