  We present single stellar population (SSP) equivalent ages, metallicities,
and abundance ratios for local elliptical galaxies derived from Hbeta, Mgb, and
<Fe> absorption line strengths. We use an extension of the Worthey (1994)
stellar population models that incorporates non-solar line-strength "response
functions" by Tripicco & Bell (1995), allowing us to correct the models for the
enhancements of Mg and other alpha-like elements relative to the Fe-peak
elements. SSP-equivalent ages of local ellipticals from Gonzalez (1993) are
found to vary widely, 1.5 < t < 18 Gyr, while metallicities [Z/H] and
enhancement ratios [E/Fe] are strongly peaked around <[Z/H]>=+0.26 and
<[E/Fe]>=+0.20 (in an aperture of radius Re/8). The enhancement ratios are
milder than previous estimates, owing to the application of non-solar abundance
corrections to both Mgb and <Fe> for the first time. Gradients in stellar
populations within galaxies are found to be mild, with SSP-equivalent age
decreasing by 25%, metallicity decreasing by <[Z/H]>=0.20 dex, and [E/Fe]
remaining nearly constant out to an aperture of radius Re/2 for nearly all
systems. Our ages have an overall zeropoint uncertainty of at least 25% due to
uncertainties in the stellar evolution prescription, the oxygen abundance, the
effect of non-solar abundances on the isochrones, and other unknowns. However,
the relative age rankings of stellar populations should be largely unaffected
by these errors. In particular, the large spread in ages appears to be real and
cannot be explained by contamination of Hbeta by blue stragglers or hot
horizontal branch stars, or by fill-in of Hbeta by emission. Correlations
between these derived SSP-equivalent parameters and other galaxy observables
will be discussed in future papers. (Abridged)
