This volume comprises the author’s account of the development of novel results in random walk theory and its applications during the fractal and chaos revolutions. The early history of probability is presented in an engaging manner, and peppered with pitfalls and paradoxes. Readers will find the introduction of Paul Lé vy’s work via Mandelbrot’s Lé vy flights which are featured uniquely as Weierstrass and Riemann random walks. Generalizations to coupled memories, internal states and fractal time are introduced at the level for graduate students. Mathematical developments are explained including Green’s functions, inverse Mellin transforms, Jacobians, and matrix methods. Applications are made to anomalous diffusion and conductivity in amorphous semiconductors and supercooled liquids. The glass transition is discussed especially for pressure effects. All along the way, personal stories are recounted and special appreciations are made to Elliott Montroll and Harvey Scher for their ever-expanding influence on the field of non-equilibrium anomalous processes that now are found in topics including disordered materials, water table processes, animal foraging, blinking quantum dots, rotating flows, optical lattices, dynamical strange attractors and strange kinetics. Key Features • Engaging history of probability theory • Step-by-step random walk equations for students • Personal stories of the novel random walk results during the fractal revolution • Tales from conferences • Unique approach to Lé vy flights • Applications to anomalous behavior in disordered materials • Derivation of stretched exponential relaxation in supercooled liquids • Pressure and temperature effects near the glass transition • Why time scales diverge near the glass transition

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