Within a unifying framework, this book covers both classical and quantum domains, along with numerous applications. The author explores the more than two centuries-old history of diffusion, expertly weaving together a variety of topics from physics, mathematics, chemistry, and biology. He describes the role of diffusion in probability theory and stochastic calculus and discusses topics in materials science and metallurgy. He also addresses the impact of translational/rotational diffusion on experimental data, covers reaction-diffusion equations in biology, and examines diffusion in the quantum domain.