[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.
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