Originally conceived some thirty years ago in the context of quantum electrodynamics, renormalization methods have progressively developed into an indispensable analytical tool used in widely varying domains of physics and applied mathematics, such as * phase transitions and critical phenomena * dynamical systems and chaos * developed turbulence * fractal structures and complex systems * percolation * polymer physics * diffusion in disordered media * measure theory and stochastic processes. By explaining the fundamental principles of renormalization theory -- such as scale invariance and universality -- which lie behind all the technical variations, this book aims to guide the reader to a more unified understanding of