This paper presents an all-sky analysis of polarization in the Cosmic Microwave Background (CMB) using spin-weighted functions. The polarization of the CMB is a second-rank symmetric and traceless tensor that can be decomposed into spin ±2 spherical harmonics. These harmonics are used to characterize the statistical properties of polarization in the CMB. The paper shows that there are two linear combinations of spin ±2 multipole moments that have opposite parities and can fully characterize the statistical properties of polarization. These combinations are the magnetic-type parity combination and the electric-type parity combination. The magnetic-type parity combination does not receive contributions from scalar modes and does not cross-correlate with either temperature or electric-type parity combination, so there are four different power spectra that fully characterize the statistical properties of the CMB. The paper presents explicit expressions for scalar and tensor modes in the form of line of sight integral solutions and numerically evaluates them for a representative set of models. These general solutions differ from the expressions obtained previously in the small scale limit both for scalar and tensor modes. The paper also discusses a method to generate and analyze all-sky maps of temperature and polarization and the optimal estimators for various power spectra and their corresponding variances. The paper discusses the power spectra for scalar and tensor modes. For scalar modes, the power spectra are derived using the Boltzmann equation and the line of sight integral solution. The power spectra for tensor modes are derived similarly, but with additional terms that account for the two independent polarizations of gravity waves. The paper also discusses the cross-correlation between different types of perturbations and shows that cross-correlation terms vanish after the integration over azimuthal angle. The paper concludes that future CMB satellite missions will produce all-sky maps of polarization and these maps will have to be analyzed using techniques similar to the one presented in this paper. Polarization measurements have the potential to provide significant additional information that will help to constrain the underlying cosmological model.This paper presents an all-sky analysis of polarization in the Cosmic Microwave Background (CMB) using spin-weighted functions. The polarization of the CMB is a second-rank symmetric and traceless tensor that can be decomposed into spin ±2 spherical harmonics. These harmonics are used to characterize the statistical properties of polarization in the CMB. The paper shows that there are two linear combinations of spin ±2 multipole moments that have opposite parities and can fully characterize the statistical properties of polarization. These combinations are the magnetic-type parity combination and the electric-type parity combination. The magnetic-type parity combination does not receive contributions from scalar modes and does not cross-correlate with either temperature or electric-type parity combination, so there are four different power spectra that fully characterize the statistical properties of the CMB. The paper presents explicit expressions for scalar and tensor modes in the form of line of sight integral solutions and numerically evaluates them for a representative set of models. These general solutions differ from the expressions obtained previously in the small scale limit both for scalar and tensor modes. The paper also discusses a method to generate and analyze all-sky maps of temperature and polarization and the optimal estimators for various power spectra and their corresponding variances. The paper discusses the power spectra for scalar and tensor modes. For scalar modes, the power spectra are derived using the Boltzmann equation and the line of sight integral solution. The power spectra for tensor modes are derived similarly, but with additional terms that account for the two independent polarizations of gravity waves. The paper also discusses the cross-correlation between different types of perturbations and shows that cross-correlation terms vanish after the integration over azimuthal angle. The paper concludes that future CMB satellite missions will produce all-sky maps of polarization and these maps will have to be analyzed using techniques similar to the one presented in this paper. Polarization measurements have the potential to provide significant additional information that will help to constrain the underlying cosmological model.