This is a collection of surveys and research papers on recent topics of interest in combinatorics, given at a conference in Matrahaza, Hungary. Originally published in journal form, it is here reissued as a book due to its special interest. It is dedicated to Paul Erdos, who attended the conference and who is represented by two articles in the collection, including one, unfinished, which he was writing on the eve of his sudden death. Erdos was one of the greatest mathematicians of his century and often the subject of anecdotes about his somewhat unusual lifestyle. A new preface, written by friends and colleagues, gives a flavour of his life, including many such stories, and also describes the broad outline and importance of his work in combinatorics and other related fields. Here is a succinct introduction to important recent ideas in combinatorics for researchers and graduate students.