This text surveys approaches and basic results of all three classes of algebraic functions: transcendental (function theoretic), algebraic-geometric, and arithmetic. Worked examples include both exercises and explanations of methods. 1933 edition.

This text surveys the approaches and basic results of all three classes of algebraic functions. Starting with a treatment of single-valued analytic functions, it introduces algebraic and rational functions and proceeds to the Riemann surface of an algebraic function, integrals of rational functions, and Abel's theorem. 1933 edition