An account from first principles is given of a number of aspects of analysis of covariance. Six different meanings of analysis of covariance are outlined and the history of this technique is sketched briefly. The development of the key formulae from the method of least squares is described, and generalizations to other distributions in the exponential family are mentioned. Special problems of application in randomized experiments and in observational studies are discussed. Finally, the decomposition of regression relations is considered along with components of covariance.