This document discusses estimating the tensor-to-scalar ratio from cosmic microwave background polarization measurements. It provides background on CMB polarization, including how density perturbations and gravitational waves create E-mode and B-mode polarization patterns. Extracting the CMB polarization signal requires cleaning foreground contamination from galactic synchrotron and dust emission. Component separation methods aim to separate the CMB, synchrotron, and dust signals using multi-frequency data. Estimating the tensor-to-scalar ratio also requires accounting for the covariance from instrument noise and residual foregrounds in power spectrum estimation and parameter constraints.