Abstract
Computing the comhomology of symmetric spaces G/K of compact types is important. Here G is a simply-connected simple compact real Lie group and K is a compact subgroup which is stable under a Cartan involution Θ of G. By a well-known result of compact symmetric spaces, the De Rham cohomology of such kind of symmetric spaces is isomorphic to the invariant space (Λ𝔭)^𝔨 with 𝔨 and 𝔭 the 1 and -1 eigen value spaces of a Cartan involution θ in the Lie algebra level. In this thesis I use an algebraic method to compute the 12 real forms of the exceptional case. And I also summarize some results for classical types.