  Close double degenerate binaries are one of the favoured progenitor channels
for type Ia supernovae, but it is unclear how many suitable systems there are
in the Galaxy. We report results of a large radial velocity survey for double
degenerate (DD) binaries using the UVES spectrograph at the ESO VLT (ESO SN Ia
Progenitor surveY - SPY). Exposures taken at different epochs are checked for
radial velocity shifts indicating close binary systems. We observed 689 targets
classified as DA (displaying hydrogen-rich atmospheres), of which 46 turned out
to possess a cool companion. We measured radial velocities (RV) of the
remaining 643 DA white dwarfs. We managed to secure observations at two or more
epochs for 625 targets, supplemented by eleven objects meeting our selection
criteria from literature. The data reduction and analysis methods applied to
the survey data are described in detail. The sample contains 39 double
degenerate binaries, only four of which were previously known. 20 are
double-lined systems, in which features from both components are visible, the
other 19 are single-lined binaries. We provide absolute RVs transformed to the
heliocentric system suitable for kinematic studies. Our sample is large enough
to sub-divide by mass: 16 out of 44 low mass targets (<= 0.45 Msun) are
detected as DDs, while just 23 of the remaining 567 with multiple spectra and
mass >0.45 Msun are double. Although the detected fraction amongst the low mass
objects (36.4 +/- 7.3%) is significantly higher than for the higher-mass,
carbon/oxygen-core dominated part of the sample (3.9 +/- 0.8%), it is lower
than the detection efficiency based upon companion star masses >= 0.05 Msun.
This suggests either companion stars of mass < 0.05 Msun, or that some of the
low mass white dwarfs are single.
