  We present a catalog of Fe, Mg, Si, Ca, and Ti abundances for 2961 red giant
stars that are likely members of eight dwarf satellite galaxies of the Milky
Way (MW): Sculptor, Fornax, Leo I, Sextans, Leo II, Canes Venatici I, Ursa
Minor, and Draco. For the purposes of validating our measurements, we also
observed 445 red giants in MW globular clusters and 21 field red giants in the
MW halo. The measurements are based on Keck/DEIMOS medium-resolution
spectroscopy combined with spectral synthesis. We estimate uncertainties in
[Fe/H] by quantifying the dispersion of [Fe/H] measurements in a sample of
stars in monometallic globular clusters. We estimate uncertainties in Mg, Si,
Ca, and Ti abundances by comparing our medium-resolution spectroscopic
measurements to high-resolution spectroscopic abundances of the same stars. For
this purpose, our DEIMOS sample included 132 red giants with published
high-resolution spectroscopy in globular clusters, the MW halo field, and dwarf
galaxies. The standard deviations of the differences in [Fe/H] and [alpha/Fe]
(the average of [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe]) between the two samples
is 0.15 and 0.16, respectively. This catalog represents the largest sample of
multi-element abundances in dwarf galaxies to date. The next papers in this
series draw conclusions on the chemical evolution, gas dynamics, and star
formation histories from the catalog presented here. The wide range of dwarf
galaxy luminosity reveals the dependence of dwarf galaxy chemical evolution on
galaxy stellar mass.
