Colliding black holes: analytic insights

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We summarize the state of the art of the ``close approximation'' to black hole collisions. We discuss results to first and second order in perturbation theory for head-on collisions of momentarily-stationary and non-stationary black holes and discuss the near-future prospect of non-axisymmetric collisions.
19 pages, crckapb.sty, 7 figures included with psfig, talk given at GR15, Poona, India, to appear in the proceedings

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