This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober’s 60th birthday, held June 22–26, 2009, in Jaca, Spain. The volume contains four parts corresponding to the four main focal points of the conference: algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements, and singularities. Together, the papers provide an overview of the current status of a broad range of topological questions in Algebraic Geometry. This book is published in cooperation with Real Sociedad Matemática Española (RSME).