This book studies three significant breakthroughs on the Steiner tree problem is achieved in the 1990s, and some important applications of Steiner tree problems in computer communication networks studied in the last fifteen years. Contents: Minimax Approach and Steiner Ratio; k-Steiner Ratio and Algorithm A better approach; Partition Scheme Geometric and Polynomial Time Approximation; Grade of Steiner Tree Problem Service; Steiner Tree Problem for Minimal Steiner points; Bottleneck Steiner Tree Problem; Steiner k- Tree and k-Path Routing Problem; Steiner Tree Problem Dyeing; Steiner Tree Problem Scheduling; Steiner Survivable Network Problem.