  This is the first of two articles in which we prove a sharp $L^p-L^2$ Fourier
restriction theorem for a large class of smooth, finite type hypersurfaces in
$\Bbb R^3$, which includes in particular all real-analytic hypersurfaces.
  The present file is a modified and extended version of an earlier file of the
same title. Some changes and corrections had become necessary, in order to make
sure that Part II is really compatible with Part I, and it is recommended to
replace the earlier version of Part I by the new one.
