In this classic text first published in German in 1918-this is a translation by HENRY L. BROSE (1890-1965) of the 1921 fourth edition-Weyl considers the role of Euclidean space in physics and the mathematics of Einstein's general theory of relativity, exploring: - foundations of affine and metrical geometry - conception of n-dimensional geometry - tensor algebra - the stationary electromagnetic field - Riemann's geometry - affinely connected manifolds - space metrics from the point of view of the Theory of Groups - relativistic geometry, kinematics, and optics - electrodynamics of moving bodies - mechanics of the principle of relativity - mass and energy - gravitational waves - concerning the interconnection of the world as a whole - and more. HERMANN KLAUS HUGO WEYL (1885-1955)was a German mathematician who spent most of his life working in Zurich, Switzerland. When the Nazi party began to gain power he fled to a job at the Institute of Advanced Study in Princeton, New Jersey where he continued to develop his representation theory. He was one of the most influential mathematicians of the 20th century. He greatly impacted theoretical physics and number theory and was the first to combine general relativity and electromagnetism