has a solution in Fn. The representation problem of quadratic forms is to determine, in an effective manner, the set of elements of F that are represented by a particular quadratic form over F . We shall discuss the case when F is a field of arithmetic interest, for instance, the field of complex numbers C, the field of real numbers R, a finite field F, and the field of rational numbers Q. The ...

I begin with a basic discussion of bilinear forms and quadratic forms. The distinction between the two is particularly important, since I do not generally assume 2 to be invertible. Then I go on to prove versions of theorems about quadratic forms that are independent of the particular coefficient field, except for distinctions based on characteristic. Eventually, I shall be interested only in q...