  We introduce LATIS, the Ly$\alpha$ Tomography IMACS Survey, a spectroscopic
survey at Magellan designed to map the z=2.2-2.8 intergalactic medium (IGM) in
three dimensions by observing the Ly$\alpha$ forest in the spectra of galaxies
and QSOs. Within an area of 1.7 deg${}^2$, we will observe approximately half
of $\gtrsim L^*$ galaxies at z=2.2-3.2 for typically 12 hours, providing a
dense network of sightlines piercing the IGM with an average transverse
separation of 2.5 $h^{-1}$ comoving Mpc (1 physical Mpc). At these scales, the
opacity of the IGM is expected to be closely related to the dark matter
density, and LATIS will therefore map the density field in the $z \sim 2.5$
universe at $\sim$Mpc resolution over the largest volume to date. Ultimately
LATIS will produce approximately 3800 spectra of z=2.2-3.2 galaxies that probe
the IGM within a volume of $4 \times 10^6 h^{-3}$ Mpc${}^3$, large enough to
contain a representative sample of structures from protoclusters to large
voids. Observations are already complete over one-third of the survey area. In
this paper, we describe the survey design and execution. We present the largest
IGM tomographic maps at comparable resolution yet made. We show that the
recovered matter overdensities are broadly consistent with cosmological
expectations based on realistic mock surveys, that they correspond to galaxy
overdensities, and that we can recover structures identified using other
tracers. LATIS is conducted in Canada-France-Hawaii Telescope Legacy Survey
fields, including COSMOS. Coupling the LATIS tomographic maps with the rich
data sets collected in these fields will enable novel studies of
environment-dependent galaxy evolution and the galaxy-IGM connection at cosmic
noon.
