A complex torus is a mathematical structure that arises from the concept of a torus, which is a doughnut-shaped surface. In the context of complex numbers, a complex torus can be formed by taking a complex vector space and identifying points that differ by lattice points. This means that the complex torus can be visualized as a flat surface that wraps around itself in two dimensions. The complex torus is often studied in the field of algebraic geometry and has connections to elliptic curves. It can be represented as the quotient of a complex vector space by a lattice, leading to interesting properties and applications in various areas of mathematics, including number theory and string theory.