Keck deep fields.: I.: Observations, reductions, and the selection of faint star-forming galaxies at redshifts z ∼ 4, 3, and 2

We introduce a very deep, R-lim similar to 27, multicolor imaging survey of very faint star-forming galaxies at z similar to 4, 3, 2.2, and 1.7. This survey, carried out on the Keck I telescope, uses the very same U(n)GRI 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 similar to 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 R <= 27-contains 427 GRI-selected z similar to 4 Lyman break galaxies, 1481 U(n)GR-selected z similar to 3 Lyman break galaxies, 2417 U(n)GR-selected z similar to 2: 2 star-forming galaxies, and 2043 U(n)GR-selected z similar to 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 similar to 4, 3, 2.2, and 1.7 samples.