  Deep rest-frame optical spectroscopy is critical for characterizing and
understanding the physical conditions and properties of the ionized gas in
galaxies. Here, we present a new spectroscopic survey called "Metal Abundances
across Cosmic Time" or $\mathcal{MACT}$, which will obtain rest-frame optical
spectra for $\sim$3000 emission-line galaxies. This paper describes the optical
spectroscopy that has been conducted with MMT/Hectospec and Keck/DEIMOS for
$\approx$1900 $z=0.1-1$ emission-line galaxies selected from our narrowband and
intermediate-band imaging in the Subaru Deep Field. In addition, we present a
sample of 164 galaxies for which we have measured the weak [OIII]$\lambda$4363
line (66 with at least 3$\sigma$ detections and 98 with significant upper
limits). This nebular emission line determines the gas-phase metallicity by
measuring the electron temperature of the ionized gas. This paper presents the
optical spectra, emission-line measurements, interstellar properties (e.g.,
metallicity, gas density), and stellar properties (e.g., star formation rates,
stellar mass). Paper II of the $\mathcal{MACT}$ survey (Ly et al.) presents the
first results on the stellar mass--gas metallicity relation at $z\lesssim1$
using the sample with [OIII]$\lambda$4363 measurements.
