  The CRESST-II cryogenic Dark Matter search, aiming at detection of WIMPs via
elastic scattering off nuclei in CaWO$_4$ crystals, completed 730 kg days of
data taking in 2011. We present the data collected with eight detector modules,
each with a two-channel readout; one for a phonon signal and the other for
coincidently produced scintillation light. The former provides a precise
measure of the energy deposited by an interaction, and the ratio of
scintillation light to deposited energy can be used to discriminate different
types of interacting particles and thus to distinguish possible signal events
from the dominant backgrounds. Sixty-seven events are found in the acceptance
region where a WIMP signal in the form of low energy nuclear recoils would be
expected. We estimate background contributions to this observation from four
sources: 1) "leakage" from the e/\gamma-band 2) "leakage" from the
\alpha-particle band 3) neutrons and 4) Pb-206 recoils from Po-210 decay. Using
a maximum likelihood analysis, we find, at a high statistical significance,
that these sources alone are not sufficient to explain the data. The addition
of a signal due to scattering of relatively light WIMPs could account for this
discrepancy, and we determine the associated WIMP parameters.

Cosmology and Nongalactic Astrophysics