The SIRTF Wide-Area Infrared Extragalactic Survey (SWIRE), the largest SIRTF Legacy program, is a wide-area imaging survey to trace the evolution of dusty, star-forming galaxies, evolved stellar populations, and active galactic nuclei (AGNs) as a function of environment, from redshifts z~3 to the current epoch. SWIRE will survey seven high-latitude fields, totaling 60-65 deg2 in all seven SIRTF bands: Infrared Array Camera (IRAC) 3.6, 4.5, 5.6, and 8 μm and Multiband Imaging Photometer for SIRTF (MIPS) 24, 70, and 160 μm. Extensive modeling suggests that the Legacy Extragalactic Catalog may contain in excess of 2 million IR-selected galaxies, dominated by (1) ~150,000 luminous infrared galaxies (LIRGs; LFIR>1011 Lsolar) detected by MIPS (and significantly more detected by IRAC), ~7000 of these with z>2 (2) 1 million IRAC-detected early-type galaxies (~2×105 with z>1 and ~10,000 with z>2) and (3) ~20,000 classical AGNs detected with MIPS, plus significantly more dust-obscured quasi-stellar objects/AGNs among the LIRGs. SWIRE will provide an unprecedented view of the evolution of galaxies, structure, and AGNs. The key scientific goals of SWIRE are (1) to determine the evolution of actively star forming and passively evolving galaxies in order to understand the history of galaxy formation in the context of cosmic structure formation; (2) to determine the evolution of the spatial distribution and clustering of evolved galaxies, starbursts, and AGNs in the key redshift range 0.5