  An exact solution of Einstein's field equations in empty space first found in
1985 by Quevedo and Mashhoon is analyzed in detail. This solution generalizes
Kerr spacetime to include the case of matter with arbitrary mass quadrupole
moment and is specified by three parameters, the mass $M$, the angular momentum
per unit mass $a$ and the quadrupole parameter $q$. It reduces to the Kerr
spacetime in the limiting case $q=0$ and to the Erez-Rosen spacetime when the
specific angular momentum $a$ vanishes. The geometrical properties of such a
solution are investigated. Causality violations, directional singularities and
repulsive effects occur in the region close to the source. Geodesic motion and
accelerated motion are studied on the equatorial plane which, due to the
reflection symmetry property of the solution, turns out to be also a geodesic
plane.
