Real forms of Jordan algebras

The problem of classification of simple Jordan algebras and Lie-Triple Systems in general had been deeply studied and satisfying results had been obtained. So, no new result on classification is in this paper, but we think that the proofs of theorems 42 and 44 are new and can be of help to understand the structure of simple real Jordan algebras better. At the end of the paper, we remark that some symmetric spaces associated to these Jordan algebras can be viewed as real forms of a complex symmetric space. (author)