1.Elementary differential geometry. 2.Lie Groups and Lie algebras. 3.Structure of semisimple Lie algebras. 4.Symmetric spaces. 5.Decomposition of symmetric spaces. 6.Symmetric spaces of the Noncompact type. 7.Symmetric spaces of the compact type. 8.Hermitian symmetric spaces. 9.On the Classification of symmetric spaces. 10.Functions on symmetric spaces.