Integral geometry, known as geometric probability in the past, originated from Buffon's needle experiment. Remarkable advances have been made in several areas that involve the theory of convex bodies. This volume brings together contributions by leading international researchers in integral geometry, convex geometry, complex geometry, probability, statistics, and other convexity related branches. The articles cover both recent results and exciting directions for future research.Contents:Volume Inequalities for Sets Associated with Convex Bodies (S Campi & P Gronchi)Integral Geometry and Alesker's Theory of Valuations (J H G Fu)Area and Perimeter Bisectors of Planar Convex Sets (P Goodey)Radon Inversion: From Lines to Grassmannians (E Grinberg)Valuations in the Affine Geometry of Convex Bodies (M Ludwig)Crofton Measures in Projective Finsler Spaces (R Schneider)Random Methods in Approximation of Convex Bodies (C Schütt)Some Generalized Maximum Principles and Their Applications to Chern Type Problems (Y J Suh)Floating Bodies and Illumination Bodies (E Werner)Applications of Information Theory to Convex Geometry (D Yang)Containment Measures in Integral Geometry (G Zhang & J Zhou)On the Flag Curvature and S-Curvature in Finsler Geometry (X Chen)and other papersReadership: Graduate students and researchers in mathematics and physics.