Cosmology, the quest concerning the Universe as a whole, has been a primary interest of human study since the beginnings of mankind. For a long time our ideas about the Universe were dominated by religious beliefs – tales of creation. Only since the advent of general relativity in 1915 have we had a scientific theory at hand that might be capable of describing the Universe. Soon after Einstein's first attempt of a static universe, Hubble and collaborators (Hubble, 1929) discovered that the observable Universe is expanding. This together with the discovery of the cosmic microwave background (CMB) by Penzias and Wilson (Nobel prize 1978) has established the theory of an expanding and cooling universe which started in a ‘big bang’.

For a long time observations that have led to the determination of cosmological parameters, such as the rate of expansion, the so-called Hubble parameter, the mean matter density of the Universe, or its curvature, have been very sparse and we could only determine the order of magnitude of these parameters.

During the last decade this situation has changed significantly and cosmology has entered an era of precision measurements. This major breakthrough is to a large extent due to precise measurement and analysis of the CMB. In this book I develop the theory which is used to analyse and understand measurements of the CMB, especially of its anisotropies and polarization, but also its frequency spectrum.