Hdelta-Selected Galaxies in the Sloan Digital Sky Survey I: The Catalog

[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