In this chapter, we present some additional information on PCA. After a reminder of some basic statistical concepts, the statistical approach to PCA is developed. This clarifies an often obscure point, a source of much discussion, on the links between PCA and Factor Analysis, in particular via the notion of probabilistic PCA. It is possible to propose a statistical approach for each of the methods in this book, but, with the exception of Correspondence Analysis, this aspect will not be developed beyond PCA. We then present a very rich topic that is often omitted in texts on PCA: the characterization of the eigenvalue distributions of random matrices, in particular the Wishart distribution and the Marčenko-Pastur semicircular law. PCA relies on the Euclidean distance to compare matrices or point clouds. An extension to other distances is still a topical but difficult issue. In vector spaces, distances are related to a norm. Such an extension has been developed in the case of Unitarily Invariant Norms, which we discuss here.