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Various problems in climate research, which require the use of advanced statistical techniques, are considered in this book. The examples emphasize the notion that the knowledge of statistical techniques alone is not sufficient. Good physical understanding of the specific problems in climate research is needed to guide the researcher in choosing the right approach to obtain meaningful answers. The second edition of this book, originally based on contributions given during a school sponsored by the European Union on the Italian island of Elba, continues to be based on these general principles. The general outline has been kept the same, covering aspects such as the examination of the observational record, stochastic climate models, analytical techniques, e.g. EOF, teleconnections and so on, but the chapters have been revised and updated, in some cases extensively, to cover the advances in the field in the years since the first edition.