The Fundamental Interactions -- The Physical Manifold -- Symmetry -- The Algebra of Observables -- Geometry of Space-Times -- Scalar Fields -- Vector, Tensor, and Spinor Fields -- Noether's Theorem -- Bundles and Connections -- Gauge Field Theory -- Gravitation.

Gravitation, electromagnetics and the two types of nuclear forces constitute the four fundamental forces of nature which regulate our everyday life.  Amazingly, they are all described by a single idea of the 19th century proposed by Bernhard Riemann, and with the exception of gravitation, these ideas have been since confirmed by high energy experiments and cosmological observations.  Geometry of the Fundamental Interactions - On Riemann's Legacy to High Energy Physics and Cosmology is a mathematical narrative of how we have come to agree on such a complex plot of nature, starting with the basic geometrical concepts and ending with hints on the perspective for cosmology. This book originated from lectures given for several years to a mixed audience of mathematicians, physicists, astronomers, engineers, philosophers and sociologists seeking to understand the basics of those interactions and how the concept of Riemann curvature came to occupy such a central position in physics.  The author takes on the challenge of making the path toward understanding both accessible and interesting to a wide audience.