This volume collects together research and survey papers written by invited speakers of the conference celebrating the 70^th birthday of László Lovász.

The topics covered include classical subjects such as extremal graph theory, coding theory, design theory, applications of linear algebra and combinatorial optimization, as well as recent trends such as extensions of graph limits, online or statistical versions of classical combinatorial problems, and new methods of derandomization.

László Lovász is one of the pioneers in the interplay between discrete and continuous mathematics, and is a master at establishing unexpected connections, “building bridges” between seemingly distant fields. His invariably elegant and powerful ideas have produced new subfields in many areas, and his outstanding scientific work has defined and shaped many research directions in the last 50 years.

The 14 contributions presented in this volume, all of which areconnected to László Lovász's areas of research, offer an excellent overview of the state of the art of combinatorics and related topics and will be of interest to experienced specialists as well as young researchers.

Introduction.- N. Alon: Lovász, Vectors, Graphs and Codes.- A. Björner: Continuous matroids revisited.- C. Borgs, J. T. Chayes, H. Cohn and L. M. Lovász: Identifiability for Graphexes and the Weak Kernel Metric.- D. Conlon, J. Fox, A. Grinshpun and Xiaoyu He: Online Ramsey Numbers and the Subraph Query Problem.- P. Csikvári: Statistical Matching Theory.- P. Diaconis: A conversation with Laci.- U. Feige: Tighter Bounds for Bipartite Matching.- T. Jordán and A. Mihálykó: Minimum Cost Globally Rigid Subgraphs.- P. Keevash: Colored and Directed Designs.- Jin Tat Lee, A. Sidford and S. S. Vempala: Efficient Convex Optimization with Oracles.- J. Nesetril and P. Osona de Mendes: Approximations of Mappings.- O. E. Raz and A. Wigderson: Derandomization Through Submodular Optimization.- A. Schrijver: Finding k Partially Disjoint Paths in a Directed Planar  Graph.- M. Simonovits and E. Szemerédi: Embedding graphs into larger graphs, results, methods and problems.