The fundamental notion of conditional independence is embedded in the theories of probability and statistics. Recent developments in this field and their importance for describing and modelling multivariate systems are the main areas covered in this book. Standard statistical practice altered radically during the 1970s and the development of log-linear models made it possible to formulate complex models for the dependences between the variables cross-classifying a contingency table. The elucidation of the family of graphical models as a subset of log-linear models unravelled the connection between these models and the fundamental notion of conditional independence. Graphical modelling is that body of statistical techniques based on fitting graphical models to data. It has the advantages of interpretation, simplification and unification. This book is directed at the student who requires a course on applied multivariate statistics unified by the concept of conditional independence, and at the research worker essentially concerned to apply the techniques of graphical modelling. It contains some exercises and solutions, many numerical examples and a few examples of a substantial practical nature.