Through the hard work of many excellent experimenters, the detection and characterization of temperature fluctuations in the cosmic microwave background is now on sure footing. Following the initial detection by the DMR instrument aboard COBE (Smoot et al., 1990), numerous ground and balloon-based detections have been made, and the first reasonably large temperature maps at angular scales of a degree have been constructed (Devlin et al., 1998). The upcoming satellites MAP and Planck promise full sky temperature maps of unprecedented resolution and sensitivity, as detailed elsewhere in these lectures. Theoretically, much of this intensive effort has been motivated by the realization that the microwave background temperature fluctuations contain a wealth of fundamental cosmological information (Eisenstein, Hu and Tegmark, 1999; Jungman et al., 1996; Zaldarriaga, Seljak, and Spergel, 1997).
Polarization of the microwave background is a different story. Polarization is expected in every cosmological model, for the simple reason that the Thomson scattering which thermalizes the radiation has a polarization-dependent cross section. But the polarization signal is generically expected to be a factor of 10 to 50 smaller than the temperature fluctuations, presenting that much greater of an experimental challenge. Only upper limits on polarization of around a part in 105 now exist, but a new generation of experiments optimized for polarization are currently being constructed, which potentially have both the raw sensitivity and the control over systematic errors necessary to make the first detection. In many ways, the experimental study of polarization today is at about the same stage that temperature was ten years ago.
This contribution aims to explain how polarization is physically characterized, how it is generated in the microwave background, the mathematical description of the associated power spectra, and the physical effects which might be probed via polarization measurements. Another elementary reference about microwave background polarization from a somewhat different perspective is White and Hu (1997).