1 Da ich erkenne, was die Welt im Innersten zusammenh* alt. Faust Concepts without intuition are empty, intuition without concepts is blind. Immanuel Kant (1724-1804) The greatest mathematicians like Archimedes, Newton, and Gauss have always been able to combine theory and applications into one. Felix Klein (1849-1925) The present comprehensive introduction to the mathematical and physical aspects of quantum ?eld theory consists of the following six volumes: Volume I: Basics in Mathematics and Physics Volume II: Quantum Electrodynamics Volume III: Gauge Theory Volume IV: Quantum Mathematics Volume V: The Physics of the Standard Model Volume VI: Quantum Gravity and String Theory. Since ancient times, both physicists and mathematicians have tried to und- stand the forces acting in nature. Nowadays we know that there exist four fundamental forces in nature: * Newton's gravitational force, * Maxwell's electromagnetic force, * the strong force between elementary particles, and * the weak force between elementary particles (e.g., the force responsible for the radioactive decay of atoms). In the 20th century, physicists established two basic models, namely, * the Standard Model in cosmology based on Einstein's theory of general relativity, and * the Standard Model in elementary particle physics based on gauge theory. 1 So that I may perceive whatever holds the world together in its inmost folds.