  This is the first of two papers describing the second data release (DR2) of
the Australia Telescope Large Area Survey (ATLAS) at 1.4 GHz, which comprises
deep wide-field observations in total intensity, linear polarization, and
circular polarization over the Chandra Deep Field-South and European Large Area
Infrared Space Observatory Survey-South 1 regions. DR2 improves upon the first
data release by maintaining consistent data reductions across the two regions,
including polarization analysis, and including differential number counts in
total intensity and linear polarization. Typical DR2 sensitivities across the
mosaicked multi-pointing images are 30 uJy/beam at approximately 12"x6"
resolution over a combined area of 6.4 square degrees. In this paper we present
detailed descriptions of our data reduction and analysis procedures, including
corrections for instrumental effects such as positional variations in image
sensitivity, bandwidth smearing with a non-circular beam, and polarization
leakage, and application of the BLOBCAT source extractor. We present the DR2
images and catalogues of components (discrete regions of radio emission) and
sources (groups of physically associated radio components). We describe new
analytic methods to account for resolution bias and Eddington bias when
constructing differential number counts of radio components.
