A mapping from a complex plane z to a complex plane w such that
w = f(z) and f'(z_o) ≠ 0 (f'(z_o) is the derivative of f at the point z_o).
f(z) is conformal everywhere in the z-plane If f'(z) ≠ 0 everywhere in the z-plane. For example, the mapping f(z) = e^z is conformal everywhere in the z-plane since f'(z) = e^z ≠ 0 everywhere.

Conformal Mapping is a technique used to tranform certain PDEs to simplier presentations.