Maximal Torus Subgroup of Connected Compact Lie groups

The maximal torus is essential to the structure and the representation of the compact Lie groups.Every connected,compact Lie groups G contains a maximal torus T.This maximal torus is unique up to conjugation,and every element of G is conjugate to the element of the maximal torus.In this thesis we offer detailed proof of main theorem on tori which take symmetric space as the main tool.