Lectures on Convex Geometry

This book providesa self-contained introduction toconvex geometry in Euclidean space.After covering the basic concepts and results, it developsBrunn-Minkowskitheory, with an exposition of mixed volumes, the Brunn-Minkowski inequality, and some of its consequences,includingthe isoperimetric inequality.Further centraltopics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations.Finally, an introduction tointegral-geometric formulas in Euclidean space is provided.The numerous exercises and the supplementary material at the end of each sectionform an essential partof the book. Convexity is an elementary and naturalconcept.It plays a key role in many mathematical fields, including functional analysis,optimization,probability theory,and stochastic geometry. Paving the way to the more advanced and specialized literature, thematerialwill beaccessible to students in the third year and can be coveredin one semester.