  We develop a unified, analytic framework for gravitational lensing by Kerr
black holes. In this first paper we present a new, general lens equation and
magnification formula governing lensing by a compact object. Our lens equation
assumes that the source and observer are in the asymptotically flat region and
does not require a small angle approximation. Furthermore, it takes into
account the displacement that occurs when the light ray's tangent lines at the
source and observer do not meet on the lens plane. We then explore our lens
equation in the case when the compact object is a Kerr black hole.
Specifically, we give an explicit expression for the displacement when the
observer is in the equatorial plane of the Kerr black hole as well as for the
case of spherical symmetry.
