ABSTRACT
We have solved classification problem for alternating bilinear spaces (see Theorem 6.2.3), but as we have mentioned in Chapter 4, for symmetric spaces the problem is much more difficult and diversified depending on the underlying field. In this chapter we prove the simplest cases of known general classification results covering symmetric spaces of dimensions 1 and 2 over an arbitrary field, and symmetric spaces of arbitrary dimensions over fields with 1 or 2 square classes. This includes classification of symmetric spaces over the fields of complex and real numbers and over all finite fields.
