In chemistry, Wiener index is a well known topological index of a molecule. It was named after the scientist H. Wiener who in 1947. established the existence of a correlation between the boiling points of paraffin and the structure of molecules. Wiener index of a graph is defined as the sum of the distances between all pairs of vertices. In this paper we deal with different ways of calculating the Wiener index of trees. First we deal with some special types of graphs, such as a complete graph, stars, paths etc. The main part of the thesis involves direct and recursive formulas for calculating the Wiener index of a tree. Some of those formulas can be applied to connected graphs.