This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling are introduced: self-similarity, long-range dependence and multi-fractals. These models are compared and related one to the other in II-1. Second, they introduce fractional integration, a mathematical tool closely related to the notion of scale invariance. Also, they define stochastic processes with prescribed scaling properties (self similar processes (II-3, locally self-similar processes (I-3), fractionally filtered processes (I-5), Iterated function systems (I-6, II-4)). A number of applications where the scaling paradigm proved fruitful are detailed: image processing (I-6, II-5), financial and stock market fluctuations (I-7), geophysics (II-5), scale relativity and fractal time-space (II-7).