Introduction to quadratic forms

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 quadratic forms over finite and local fields, which is why I can get by with such a brief discussion of the general theory here. I’ll discuss these topics elsewhere, but thought that some general background would be useful.