The design of approximation algorithms for spanning tree problems has become an exciting and important area of theoretical computer science and also plays a significant role in emerging fields such as biological sequence alignments and evolutionary tree construction. While work in this field remains quite active, the time has come to collect under

Introduction. Minimum Spanning Trees. Shortest-Paths Trees. Minimum Routing Cost Spanning Trees. Optimal Communication Spanning Trees. Balancing the Tree Costs. Steiner Trees and Some Other Problems.