This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Ji¿í Matoüek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition ¿ something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Ji¿í Matoüek¿s numerous areas of mathematical interest.