Wave polarization and polarimetry play vital roles in radar target identification comprising the three phases of target detection, discrimination, and recognition. This chapter presents an introduction to radar polarimetry emphasizing the polarization behavior as described by the scattering matrix. After a brief review of linear, circular, and elliptical polarization and the geometrical parameters of polarization ellipse, such as tilt and ellipticity angles and axial ratio, Stokes parameters and scattering matrices are introduced and explained using examples on canonical targets. The projection of polarization states on the Poincare sphere is discussed. The transformation of the scattering matrix from one polarization state basis to another (e.g., linear to circular and vice versa) is derived. Unitary transformations are applied to the scattering matrix for fully polarized targets and eigen-polarization states corresponding to maximum and minimum backscattered power are derived. The location of null polarization states on the Poincare sphere is discussed, and the Huynen polarization fork is introduced as a useful tool in the visualization of optimal polarimetric parameters. Stokes reflection or Mueller matrix is derived for partially polarized waves. The distinction between Kennaugh's and Huynen's formulations of the target scattering matrix (partially polarized case) is discussed. To demonstrate the application of radar polarimetry, the scattering matrix measurements of a cone with grooves (resembling a missile reentry vehicle) are processed to extract key features such as specular scattering and edge contributions, and the usefulness of polarimetric signatures to discriminate between coated and uncoated bodies is discussed. The polarimetric behavior of precipitation clutter, sea clutter, and ground clutter is also discussed. A radar instrumentation setup for scattering matrix measurement in block diagram form is described, and implications on the setup imposed by colocation of transmit and receive antennas for monostatic measurements and the need to measure amplitude and phase of each orthogonal channel relative to a coherent source are discussed.