Diffusion and Wave Phenomena takes readers on a journey through some of the most pivotal discoveries in physics, chemistry, and molecular biology over the last two centuries. It explores scientific breakthroughs that are rightly considered 'Rosetta Stones' in their respective fields—discoveries through which scientists have deciphered nature's fundamental principles.The book weaves a historical and conceptual narrative around two quantitative frameworks: diffusion phenomena and wave phenomena. These two topics have shaped our understanding of heat conduction, electromagnetism, quantum mechanics, and several key aspects of molecular biology. Much of the book concerns the discovery of the DNA double helix, the genetic code, and the sequencing of genomes. Each section introduces a major discovery, placing it in its historical context while graphically explaining its scientific significance in a manner accessible to students and researchers in both the quantitative sciences and the history of science.The work bridges physics, mathematics, biochemistry, and biology, offering a rare integrative perspective that underlines the unity of the 'hard' sciences. A distinctive feature of the book is the recourse to two of the most important partial differential equations of mathematics, the diffusion equation and the wave equation. These are derived, solved, and explained in a rigorous yet didactic way, in their historical context, for a great diversity of topics. They provide a continuous thread linking the 'Rosetta Stone' discoveries that have advanced the field under consideration. The reference to the Rosetta Stone is not merely metaphorical: the artefact itself was studied by Joseph Fourier and Thomas Young, the respective founders of diffusion theory and wave theory, which form the twin pillars of this book.