This paper presents an all-sky analysis of polarization in the Cosmic Microwave Background (CMB) using spin-weighted functions. The authors decompose linear polarization into spin ±2 spherical harmonics, which are analogous to temperature spherical harmonics. They show that two linear combinations of these multipole moments, with opposite parities, can fully characterize the statistical properties of CMB polarization. These combinations, denoted as $E$ and $B$, differ from the usual electric and magnetic fields in that they are rotationally invariant and do not cross-correlate with each other or with temperature. The paper derives explicit expressions for the power spectra of $T$, $E$, $B$, and their cross-correlation, valid for any angular scale. These expressions are derived using the line of sight integral solution of the photon Boltzmann equation and are compared with small-scale approximations, showing that the exact solutions are more accurate, especially for large angular scales. The authors also discuss methods for generating and analyzing all-sky maps of polarization and temperature, and provide optimal estimators for various power spectra and their variances. The results are relevant for future CMB satellite missions, which will measure polarization over the entire sky with high angular resolution, providing valuable information on cosmological parameters, particularly on large angular scales.This paper presents an all-sky analysis of polarization in the Cosmic Microwave Background (CMB) using spin-weighted functions. The authors decompose linear polarization into spin ±2 spherical harmonics, which are analogous to temperature spherical harmonics. They show that two linear combinations of these multipole moments, with opposite parities, can fully characterize the statistical properties of CMB polarization. These combinations, denoted as $E$ and $B$, differ from the usual electric and magnetic fields in that they are rotationally invariant and do not cross-correlate with each other or with temperature. The paper derives explicit expressions for the power spectra of $T$, $E$, $B$, and their cross-correlation, valid for any angular scale. These expressions are derived using the line of sight integral solution of the photon Boltzmann equation and are compared with small-scale approximations, showing that the exact solutions are more accurate, especially for large angular scales. The authors also discuss methods for generating and analyzing all-sky maps of polarization and temperature, and provide optimal estimators for various power spectra and their variances. The results are relevant for future CMB satellite missions, which will measure polarization over the entire sky with high angular resolution, providing valuable information on cosmological parameters, particularly on large angular scales.