This chapter introduces a number of data-analytic procedures of normal distribution theory. Like most procedures based on normal theory, they depend on the values of the sample means, variances and covariances, and so have a heuristic attraction independent of the distributional assumptions. Thus, it could be argued that these procedures are useful methods for the analysis of any data, although, of course, significance levels are only valid when the distributional assumptions apply. The discrimination problem in its most basic form arises when it is required to allocate an individual to one or other of two populations on the basis of a measurement of a p-dimensional random variable on the individual. It is presumed that the random variable has a different distribution for each of the populations. When the losses due to misclassification can be quantified, the problem may be tackled by decision theory. When the covariance matrices are not equal, the discriminant function will be quadratic in x.