This thesis investigates multi-source spanning tree problems where, given a graph with edge weights and a subset of the nodes defined as sources, the object is to find a spanning tree of the graph that minimizes some distance related cost metric. This problem can be used to model multicasting in a network where messages are sent from a collection of senders, and the goal is to reach every receiver within minimum total cost. In this model, it is assumed that communication takes place along the edges of a single spanning tree. For a set of possible cost metrics for creating such a spanning tree, this thesis determines whether the problem is NP-hard; otherwise, it demonstrates the existence of an efficient algorithm to find an optimal tree.