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This handbook provides an up-to-date survey of current research topics and applications of time series analysis methods written by leading experts in their fields. It covers recent developments in linear and non-linear, as well as stochastic and deterministic analysis methods and their cross-fertilization between Mathematics, Physics, and Engineering. Each chapter comprises both methodological aspects and applications to time series from real world complex systems, such as the human brain or Earth's climate. Covering an exceptionally broad spectrum of topics, beginners, experts and practitioners who seek to understand the latest developments will profit from this handbook.