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This book exposes the fundamental theory for non-standard diffusion problems in movement ecology. Lévy processes and anomalous diffusion have shown to be both powerful and useful tools in describing qualitatively and quantitatively a wide variety of spatial population ecological phenomena and dynamics, such as invasions fronts and search strategies. §Adopting a self-contained, textbook-style presentation the authors provide the elements of statistical physics and stochastic processes on which the modelling of movement ecology is based and introduce in a systematic way the physical characterization of ecological processes at the microscopic, mesoscopic and macroscopic levels of description. The explicit distinction of these description levels and their interrelation is particularly suitable to cope with the broad spectrum of space and time scales involved in bio-ecological problems. §Containing numerous exercises (with solutions), this text is aimed at graduate students and newcomers in this field at the interface of theoretical ecology, mathematical biology and physics.