This is the report of the presentation I gave for the Group Theory Course.

It is basically a complete proof of a very important and curious result in compact connected groups which states that all maximal connected abelian subgroups( tori) are conjugate to each other and the union of all these conjugates cover the entire set.

The proof is quite long and somewhat involved but nonetheless there are some very interesting ideas that go into it. A glimpse of that can be seen in the section where I have proved some theorems that would be required in the main proof.

Maximal Tori In Compact Connected Groups