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In applied and pure sciences, the structural properties of groups are increasingly utilised to find better solutions in statistical sciences. Modern computers make statistical methods with large numbers of variables feasible. Invariance is a mathematical term for symmetry, and many statistical problems exhibit such properties. In statistical analysis with large numbers of variables, the invariance approach is becoming increasingly popular and useful because of its ability and usefulness in deriving better statistical procedures.In this book, Multivariate Statistical Inference is presented through Invariance.