Among a number of wonderful ideas we owe to Riemann, the idea of Riemann surface is, without doubt, the most beautiful, everlasting, intensively developing, and unifying. It fertilizes a number of other ideas, penetrating the whole body of mathematics and, in turn, many branches of physics. This idea originated from the germ of algebraic functions or elliptic integrals (differentials) and their local inverses: elliptic functions.