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We introduce a very deep, lim ~ 27, multicolor imaging survey of very faint star-forming galaxies at z ~ 4, 3, 2.2, and 1.7. This survey, carried out on the Keck I telescope, uses the very same U n G I filter system that is employed by the Steidel team to select galaxies at these redshifts and thus allows us to construct identically selected but much fainter samples. However, our survey reaches ~1.5 mag deeper than the work of Steidel and his group, letting us probe substantially below the characteristic luminosity L * and thus study the properties and redshift evolution of the faint component of the high- z galaxy population. The survey covers 169 arcmin 2 in three spatially independent patches on the sky and—to ≤ 27—contains 427 G I -selected z ~ 4 Lyman break galaxies, 1481 U n G -selected z ~ 3 Lyman break galaxies, 2417 U n G -selected z ~ 2.2 star-forming galaxies, and 2043 U n G -selected z ~ 1.7 star-forming galaxies. In this paper, the first in a series, we introduce the survey, describe our observing and data reduction strategies, and outline the selection of our z ~ 4, 3, 2.2, and 1.7 samples.
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