The first four chapters of this presentation on classical function theory convey central results and methods of complex analysis in one variable with minimal conceptual effort and based on limited prior knowledge. They culminate in a proof of the small Riemann mapping theorem and a characterization of simply connected domains. Additional topics include elliptic functions (Weierstrass and Jacobian approaches), the elementary theory of modular forms in one variable, as well as applications of these functions to number theory, including a proof of the prime number theorem. Plus: over 400 exercises with solutions.