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.
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