Geometrodynamics of Gauge Fields : On the Geometry of Yang Mills and Gravitational Gauge Theories This monograph aims to provide a unified geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang Mills theories instanton solutions and topological invariants are included. By transferring these concepts to local space time symmetries generalizations of Einsteins theory of gravity arise in a Riemann Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory the Rainich geometrization of the Einstein Maxwell system and higher dimensional non abelian Kaluza Klein theories are developed. Since the discovery of the Higgs boson concepts of spontaneous symmetry breaking in gravity have come again into focus and in this revised edition these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang Mills some new progress in its topological form is presented. After symmetry breaking Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non propagating topological ghosts is developed in some detail. Preface 1 Historical background 2 Geometry of gauge fields 3 Maxwell and Yang Mills theory 4 Gravitation as a gauge theory 5 Einstein Cartan theory 6 Teleparallelism 7 Yang’s theory of gravity 8 BRST quantization of gravity 9 Gravitational instantons 10 Three dimensional gravity 11 Spinor bundles 12 Chiral anomalies 13 Topological SL(5;R) gauge invariant action 14 Geometrodynamics and its extensions 15 Color Geometrodynamics 16 Geometrodynamical model of quark confinement Appendix A Notation and mathematical terms Appendix B Calculus of exterior forms Appendix C Lie groups.