The structures of physics, in general, are studied by using simplified geometry on objects that are actually irregular and highly complex. The complex morphology and dynamics of many phenomena are lost when this is done. Benoît B. Mandelbrot, author of the preface, has spent 20 years studying the phenomena required to model these structures in all their dimensions. These structures are called fractals, and are characterized by their invariance of scale: each figure is composed of figures which are virtually identical and which are in turn composed of virtually identical figures, and so on indefinitely. Fractals are the result of 70 years of research in many fields; what they reveal has pertinence to physics of materials, mechanics of fluids, functional anatomy, plant morphology, geomorphology, astrophysics, and other disciplines. This book highlights the structures of fractals in related disciplines: turbulence, chaos, fracture, percolation, diffusion fronts, aggregation, phase transitions, particle trajectories. The author describes in detail the dynamic aspects of transport phenomena in the field of fractals. Intended for students of physics and chemistry in their second or third year, this book is also addressed to researchers and engineers interested in the trends of contemporary physics as they relate to real applications. An extensive bibliography directs the reader to additional material on specific topics.