In the first half of the 19th century geometry changed radically, and withina century it helped to revolutionizeboth mathematics and physics. It also put the epistemologyand the philosophy of science on a new footing. In thisvolume a sound overview of this development is given byleading mathematicians, physicists, philosophers, andhistorians of science. This interdisciplinary approach givesthis collection a unique character. It can be used byscientists and students, but it also addresses a generalreadership.