The Book Concerned on Applying different enumeration techniques of spanning Trees of a graph Such as Direct counting Method, Conditioning method, Deletion Method, Inclusion-exclusion Method, recurrence relation Method, Cryptographic Method.We also Used a well known Deletion-contraction theorem to count spanning trees of a graph with very Small number of vertices and edges. For any graph, we developed a ways of Counting spanning trees Combinatorical Approach and Matrix Algebra Method. we also Noted that Matrix -Tree Theorem ,Cayley's and Scoin's Formula are vital Methods of Counting spanning trees of a graph and brief Discussion is included in this Book..