The study of the power-spectrum of spatial fluctuations in the Cosmic Microwave Background Radiation provides one of the most important means of confronting theories of the origin of the large-scale structure of the Universe with observation. The problem addressed in this chapter is how to relate the fluctuations in the dark and baryonic matter on the last scattering surface at the epoch of recombination to the intensity fluctuations which they imprint upon the background radiation. Of crucial importance in this calculation is the ionisation state of the intergalactic gas during the epochs when it changed from being a fully ionised plasma to a neutral gas. We have dealt with a number of important aspects of the physics of this process in Sect. 9.3, but now we need to understand these in a little more detail.