  We present the KMOS-CLASH (K-CLASH) survey, a K-band Multi-Object
Spectrograph (KMOS) survey of the spatially-resolved gas properties and
kinematics of 191 (predominantly blue) H$\alpha$-detected galaxies at $0.2
\lesssim z \lesssim 0.6$ in field and cluster environments. K-CLASH targets
galaxies in four Cluster Lensing And Supernova survey with Hubble (CLASH)
fields in the KMOS $IZ$-band, over $7'$ radius ($\approx2$-$3$ Mpc)
fields-of-view. K-CLASH aims to study the transition of star-forming galaxies
from turbulent, highly star-forming disc-like and peculiar systems at
$z\approx1$-$3$, to the comparatively quiescent, ordered late-type galaxies at
$z\approx0$, and to examine the role of clusters in the build-up of the red
sequence since $z\approx1$. In this paper, we describe the K-CLASH survey,
present the sample, and provide an overview of the K-CLASH galaxy properties.
We demonstrate that our sample comprises star-forming galaxies typical of their
stellar masses and epochs, residing both in field and cluster environments. We
conclude K-CLASH provides an ideal sample to bridge the gap between existing
large integral-field spectroscopy surveys at higher and lower redshifts. We
find that star-forming K-CLASH cluster galaxies at intermediate redshifts have
systematically lower stellar masses than their star-forming counterparts in the
field, hinting at possible "downsizing" scenarios of galaxy growth in clusters
at these epochs. We measure no difference between the star-formation rates of
H$\alpha$-detected, star-forming galaxies in either environment after
accounting for stellar mass, suggesting that cluster quenching occurs very
rapidly during the epochs probed by K-CLASH, or that star-forming K-CLASH
galaxies in clusters have only recently arrived there, with insufficient time
elapsed for quenching to have occured.
