A Riemann surface is a one-dimensional complex manifold that allows for the study of complex functions in a more geometric way. It provides a way to visualize multi-valued functions, such as the square root or logarithm, by representing them as surfaces where each point corresponds to a unique value of the function. These surfaces are named after the mathematician Bernhard Riemann, who contributed significantly to complex analysis. Riemann surfaces can be constructed by "gluing" together simpler surfaces, and they play a crucial role in various areas of mathematics, including algebraic geometry and string theory.