Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Geometry of continuing fractions has applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. This module introduces a new geometric vision of continued fractions. Students will study how classical theorems can be visualized via modern techniques of integer geometry.