  The problem of the classification of the indefinite binary quadratic forms
with integer coefficients is solved introducing a special partition of the de
Sitter world, where the coefficients of the forms lie, into separate domains.
Every class of indefinite forms, under the action of the special linear group
acting on the integer plane lattice, has a finite and well defined number of
representatives inside each one of such domains. This property belongs
exclusively to rational points on the one-sheeted hyperboloid. In the second
part we will show how to obtain the symmetry type of a class as well as its
number of points in all domains from a sole representative of that class.
