Progress and visions in quantum theory in view of gravity : bridging foundations of physics and mathematics Algebraic Quantum Field Theory Causal Fermion Systems: An Elementary Introduction To Physical Ideas and Mathematical Concepts Quantum Spacetime and the Renormalization Group: Progress and Visions Proposal 42 A new Storyline for the Universe based on the Causal Fermion Systems Framework Energy Inequalities in Interacting Quantum Field Theories Snyder de Sitter meets the Grosse Wulkenhaar Model Fakeons Quantum Gravity And The Correspondence Principle Implementation of the Quantum Equivalence Principle The D CTC Condition in Quantum Field Theory Remarks on Matter Gravity Entanglement Entropy Information Loss and Events A Generally Covariant Measurement Scheme for Quantum Field Theory in Curved Spacetimes Understanding “Understanding”. This book focuses on a critical discussion of the status and prospects of current approaches in quantum mechanics and quantum field theory in particular concerning gravity. It contains a carefully selected cross section of lectures and discussions at the seventh conference “Progress and Visions in Quantum Theory in View of Gravity” which took place in fall 2018 at the Max Planck Institute for Mathematics in the Sciences in Leipzig. In contrast to usual proceeding volumes instead of reporting on the most recent technical results contributors were asked to discuss visions and new ideas in foundational physics in particular concerning foundations of quantum field theory. A special focus has been put on the question of which physical principles of quantum (field) theory can be considered fundamental in view of gravity. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up to date overview of a fascinating active research area.