A Riemann surface is a one-dimensional complex manifold that allows for the extension of complex functions beyond their traditional boundaries. They enable the visualization of multi-valued functions, like the square root or logarithm, in a way that is both structured and manageable. By providing a means to resolve branch points and identify different sheets of a function, Riemann surfaces play a crucial role in understanding conformal mappings, analytic properties, and more complex relationships between functions.
congrats on reading the definition of Riemann Surface. now let's actually learn it.