This volume presents surveys, written by experts in the field, on various classical and the modern aspects of Hilbert geometry. They are assuming several points of view: Finsler geometry, calculus of variations, projective geometry, dynamical systems, and others. Some fruitful relations between Hilbert geometry and other subjects in mathematics are emphasized, including Teichmüller spaces, convexity theory, Perron-Frobenius theory, representation theory, partial differential equations, coarse geometry, ergodic theory, algebraic groups, Coxeter groups, geometric group theory, Lie groups and discrete group actions. The _Handbook_ is addressed to both students who want to learn the theory and researchers working in the area. |