The Atacama Cosmology Telescope: A Catalog of >4000 Sunyaev-Zel'dovich Galaxy Clusters

We present a catalog of 4195 optically confirmed Sunyaev-Zel'dovich (SZ) selected galaxy clusters detected with signal-to-noise ratio >4 in 13,211 deg(2) of sky surveyed by the Atacama Cosmology Telescope (ACT). Cluster candidates were selected by applying a multifrequency matched filter to 98 and 150 GHz maps constructed from ACT observations obtained from 2008 to 2018 and confirmed using deep, wide-area optical surveys. The clusters span the redshift range 0.04 < z < 1.91 (median z = 0.52). The catalog contains 222 z > 1 clusters, and a total of 868 systems are new discoveries. Assuming an SZ signal versus mass-scaling relation calibrated from X-ray observations, the sample has a 90% completeness mass limit of M-500c > 3.8 x 10(14) M, evaluated at z = 0.5, for clusters detected at signal-to-noise ratio >5 in maps filtered at an angular scale of 24. The survey has a large overlap with deep optical weak-lensing surveys that are being used to calibrate the SZ signal mass-scaling relation, such as the Dark Energy Survey (4566 deg(2)), the Hyper Suprime-Cam Subaru Strategic Program (469 deg(2)), and the Kilo Degree Survey (825 deg(2)). We highlight some noteworthy objects in the sample, including potentially projected systems, clusters with strong lensing features, clusters with active central galaxies or star formation, and systems of multiple clusters that may be physically associated. The cluster catalog will be a useful resource for future cosmological analyses and studying the evolution of the intracluster medium and galaxies in massive clusters over the past 10 Gyr.