The VideoMath Festival is a collection of the juried mathematical videos presented at ICM '98, the International Congress of Mathematicians in Berlin. The videos are winners of a worldwide competition, in which the international jury evaluated their mathematical relevance, technical quality, and artistic imagination. The mathematical themes include problems in topology and geometry and their recent solutions, visualizations of classical ideas of Archimedes, Eratosthenes, Pythagoras, and Fibonacci, topics in high school mathematics, and applications of modern numerical methods to real world simulations. The videos target a general scientific audience interested in mathematical topics and their visualization. They are useful for initiating discussions, and to stimulate further research. The VideoMath collection is eminently suitable for school and university instruction. It provides an entertaining and informative look into current research in pure, applied and didactic mathematics.