​This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include:  graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.

Imre Bárány: Tensors, colours, octahedral.- Maria Chudnovsky: Cliques and stable sets in undirected graphs.- Mauro Di Nasso: A taste of nonstandard methods in combinatorics of numbers.- Béla Bollobás, Zoltán Füredi, Ida Kantor, G. O. H. Katona and Imre Leader: A coding problem for pairs of subsets.- Jirí Matousek: String graphs and separators.- Jaroslav Nesetril and Patrice Ossona de Mendez: On first-order definable colorings.- Ryan Schwartz and József Solymosi: Combinatorial applications of the subspace theorem.- Peter Hegarty and Dmitry Zhelezov: Can connected commuting graphs of finite groups have arbitrarily large diameter?

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