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We present the temperature and polarization angular power spectra of the CMB measured by the Atacama Cosmology Telescope (ACT) from 5400 deg(2) of the 2013-2016 survey, which covers >15000 deg(2) at 98 and 150 GHz. For this analysis we adopt a blinding strategy to help avoid confirmation bias and, related to this, show numerous checks for systematic error done before unblinding. Using the likelihood for the cosmological analysis we constrain secondary sources of anisotropy and foreground emission, and derive a "CMB-only" spectrum that extends to l = 4000. At large angular scales, foreground emission at 150 GHz is similar to 1% of TT and EE within our selected regions and consistent with that found by Planck. Using the same likelihood, we obtain the cosmological parameters for Lambda CDM for the ACT data alone with a prior on the optical depth of tau = 0.065 +/- 0.015. Lambda CDM is a good fit. The best-fit model has a reduced chi(2) of 1.07 (PTE = 0.07) with H-0 = 67.9 +/- 1.5 km/s/Mpc. We show that the lensing BB signal is consistent with Lambda CDM and limit the celestial EB polarization angle to psi(P) = 0.07 degrees +/- 0.09 degrees. We directly cross correlate ACT with Planck and observe generally good agreement but with some discrepancies in TE. All data on which this analysis is based will be publicly released. ; National Science Foundation (NSF) AST0408698 AST-0965625 AST-1440226 PHY0355328 PHY-0855887 PHY-1214379 Princeton University University of Pennsylvania Canada Foundation for Innovation CFI under the Compute Canada Government of Ontario Ontario Research Fund \ Research Excellence University of Toronto Simons Foundation National Aeronautics & Space Administration (NASA) NNX13AE56G NNX14AB58G National Institute of Standards & Technology (NIST) - USA Cornell Presidential Postdoctoral Fellowship Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) BASAL CATA AFB-170002 National Science Foundation (NSF) AST-1814971 AST1454881 AST-1513618 AST-1907657 AST-1910021 National Research Foundation - South Africa STFC Ernest Rutherford Fellowship ST/M004856/2 STFC Consolidated Grant ST/S00033X/1 Horizon 2020 ERC Starting Grant 849169 Dicke Fellowship Mishrahi and Wilkinson funds CIfAR's Gravity & the Extreme Universe Program CGIAR Dunlap Institute