Early number systems and symbols; mathematics in early civilizations; the beginnings of Greek mathemaics; the first Alexandrian school - Euclid; the second Alexandrian school - Diophantus; the first awakening - Fibonacci; the cubic controversy - Cardan and Tartaglia; the mechanical world - Descartes and Newton; the development of probability theory - Pascal, Bernoulli and Laplace; the renaissance of number theory - Fermat, Eutler and Gauss; non-euclidean geometry - Bolyai and Lobachevesky; the theory of sets - Georg Cantor; extensions and generalizations - Hardy, Hausdorff and Noether; the Greek alphabet; solutions to selected problems.