This thesis presents the measurement of the cosmic microwave background (CMB) power spectrum for the Atacama Cosmology Telescope (ACT) experiment and its polarized upgrade, ACTPol. I present the tools that I have developed for constructing unbiased and nearly optimal statistical estimators. I discuss how to separate the cosmological and the astrophysical signal and how to characterize instrumental systematics. The goal of this work is to obtain accurate power spectra measurement that can be used for cosmological parameter estimation. I first present the analysis of the complete ACT data set. The high resolution of the telescope allows us to recover power spectra to ℓ = 10000. I report the measurement of the power spectra at 148 GHz and 218 GHz, as well as the cross-frequency spectrum between the two channels. The power spectrum measurement is consistent with the ΛCDM model and a basic foreground model. I then present the cross correlation of maps from the Atacama Cosmology Telescope with maps from the Planck satellite in two overlapping regions covering 592 square degrees. I find excel- lent agreement between the two datasets at both frequencies, quantified using the variance of the residuals between the ACT power spectra and the ACT×Planck cross-spectra. The next generation of CMB experiments are focused on measuring its polarization. I present efficient algorithms for CMB lensing simulation and power spectrum estimation for flat-sky CMB polarization maps. Finally, I discuss the first temperature and polarization power spectra measurement from the ACTPol experiment. They are the first attempt to measure the polarization of the CMB at high resolution.