  We present redshifts for 2753 low-redshift galaxies between $0.03 \lesssim
z_{\rm spec}\lesssim0.5$ with 18 $\leq$ $r$ $\leq$ 22 obtained with Hectospec
at the Multi-Mirror Telescope (MMT). The observations targeted the XMM-LSS,
ELAIS-N1 and DEEP2-3 fields, each of which covers $\sim$ 1 deg$^2$. These
fields are also part of the recently completed CFHT Large Area U-band Deep
Survey (CLAUDS) and on-going Hyper Suprime-Cam deep fields surveys. The
efficiency of our technique for selecting low-redshift galaxies is confirmed by
the redshift distribution of our sources. In addition to redshifts, these high
S/N spectra are used to measure ages, metallicities, and nuclear activity
levels. In combination with the photometric catalogue in $u$, $g$, $r$, $i$,
$z$, $y$ down to 27 AB mag, we are able to study the galaxy population down to
stellar masses of $\sim$ 10$^8 M_\odot$ . This paper presents the observational
strategy, the reduction procedure and properties of the galaxy sample.
