A book for all those with an interest in mathematics. The author, the late Alfred Renyi, an outstanding Hungarian mathematician, worked throughout his life to inspire others with his own love for the subject. The first paper in the book, "On the mathematical notion of information", is written in the form of a diary, as though a university student just beginning the study of information theory is writing down his thoughts. The book also contains papers on games of chance, the teaching of probability theory and the mathematical theory of trees. Throughout, Renyi's intention is to show what mathematics is, how it can contribute to our everyday life, and how it can further the development of our thinking.