[Abridged] We present here a new and homogeneous sample of 3340 galaxies
selected from the Sloan Digital Sky Survey (SDSS) based solely on the observed
strength of their Hdelta absorption line. These galaxies are commonly known as
post-starburst'' or E+A’’ galaxies, and the study of these galaxies has
been severely hampered by the lack of a large, statistical sample of such
galaxies. In this paper, we rectify this problem by selecting a sample of
galaxies which possess an absorption Hdelta equivalent width of EW(Hdelta_max)
- Delta EW(Hdelta_max) > 4A from 106682 galaxies in the SDSS. We have performed
extensive tests on our catalog including comparing different methodologies of
measuring the Hdelta absorption and studying the effects of stellar absorption,
dust extinction, emission-filling and measurement error. The measured abundance
of our Hdelta-selected (HDS) galaxies is 2.6 +/- 0.1% of all galaxies within a
volume-limited sample of 0.05<z<0.1 and M(r*)<-20.5, which is consistent with
previous studies of such galaxies in the literature. We find that only 25 of
our HDS galaxies in this volume-limited sample (3.5+/-0.7%) show no evidence
for OII and Halpha emission, thus indicating that true E+A (or k+a) galaxies
are extremely rare objects at low redshift, i.e., only 0.09+/-0.02% of all
galaxies in this volume-limited sample are true E+A galaxies. In contrast,
89+/-5% of our HDS galaxies in the volume-limited sample have significant
detections of the OII and Halpha emission lines. We find 27 galaxies in our
volume-limited HDS sample that possess no detectable OII emission, but do
however possess detectable Halpha emission. These galaxies may be dusty
star-forming galaxies. We provide the community with this new catalog of
Hdelta-selected galaxies to aid in the understanding of these galaxies.