This book collects carefully selected papers written by invited and plenary speakers of the XVth International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles that were stimulated by the conference discussions, the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts in Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory and Random Matrices are introduced by prominent mathematical physicists and mathematicians, covering the fields Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help participants of the XVth ICMP to get an update on the most recent developments in their field, and give a great overview on actual and future research directions to readers with a general interest in mathematical physics.