Permutation testing for multivariate stochastic ordering and ANOVA designs is a fundamental issue in many scientific fields such as medicine, biology, pharmaceutical studies, engineering, economics, psychology, and social sciences. This book presents new advanced methods and related R codes to perform complex multivariate analyses. The prerequisites are a standard course in statistics and some background in multivariate analysis and R software. Dario Basso is a Post Doctoral Fellow at the Department of Management and Engineering of University of Padova His main research interests include permutation tests and design of experiments. Fortunato Pesarin is Full Professor of Statistics at the Department of Statistics of the University of Padova. His main research interests include nonparametric methods, bootstrap methods, and permutation tests. He has published a leading book on multivariate permutation tests based on nonparametric combination methodology. Luigi Salmaso is Associate Professor of Statistics at the Department of Management and Engineering of the University of Padova. His main research interests include permutation methods, multiple tests, and design of experiments. He has published more than 70 papers on permutation methods and design of experiments in international peer-reviewed journals. Aldo Solari is a Post Doctoral Fellow at the Department of Chemical Process Engineering of the University of Padova. His main research interest is resampling-based multiple testing methods.