<P>Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, and combinatorial geometry. The recent volume contains
high level surveys on these topics with authors mostly being invited speakers for the conference "Horizons of Combinatorics" held in Balatonalmadi, Hungary in 2006. The collection gives an overview of recent trends and results
in a large part of combinatorics and related topics.</P>