Multivariate data consist of observations on several different variables for a number of individuals or objects. Data of this type arise in all branches of science, ranging from psychology to biology, and methods of analysing multivariate data constitute an increasingly important area of statistics. This chapter provides some examples of multivariate data. They are: exam results, a nutritional study, medical data, and other examples. Principal component analysis aims to transform the observed variables to a new set of variables which are uncorrelated and arranged in decreasing order of importance. Factor analysis has somewhat similar aims but assumes a proper statistical model which takes explicit account of error. The chapter provides some of the definitions and results which are particularly useful in multivariate analysis. A matrix is a rectangular array of elements. If it has m rows and n columns, it is said to be of order (m × n).