  We study the wave equation in a bounded domain or on a compact Riemannian
manifold with boundary. Assume that we are given the hyperbolic
Neumann-to-Dirichlet map on the boundary corresponding to physical boundary
measurements. We consider how to focus waves, that is, how to find Neumann
boundary values so that at a given time the corresponding wave converges to a
delta distribution $\delta_y$ while the time derivative of the wave converges
to zero. Such boundary value are generated by an iterative sequence of
measurements. In each iteration step we apply time reversal and other simple
operators to measured data and compute boundary values for the next iteration
step. The key feature of the algorithm is that it does not require knowledge of
the coefficients in the wave equation, that is, the material parameters inside
the media. However, we assume that the point $y$ where the wave focuses is
known in travel time coordinates.
