Conformal Mapping — L. Bieberbach, trans. F. Steinhardt, Chelsea Publishing 1953

Conformal Mapping by L. Bieberbach, translated by F. Steinhardt of Columbia University, is the English-language edition of Bieberbach's authoritative German text Konforme Abbildung, published by Chelsea Publishing Company of New York in 1953. It stands as one of the most important classical treatments of conformal mapping in the mathematical literature.

Conformal mapping is a technique in complex analysis by which angle-preserving transformations of the complex plane are used to solve problems in mathematical physics, fluid dynamics, electrostatics, and engineering. Bieberbach's text develops the theory systematically from its foundations in complex function theory, covering the Riemann mapping theorem, the Schwarz-Christoffel transformation, the mapping of polygonal regions, and the behavior of conformal maps at boundaries. The treatment is rigorous and comprehensive, reflecting Bieberbach's mastery of the subject, and the translation by Steinhardt renders the mathematics with clarity and fidelity to the original German.

Ludwig Bieberbach (1886–1982) was one of the most technically gifted German mathematicians of the early 20th century, whose name is permanently attached to the Bieberbach conjecture — one of the most celebrated problems in complex analysis, posed by Bieberbach in 1916 and finally proved by Louis de Branges in 1985. His work on conformal mapping and geometric function theory was foundational, and this text distills decades of research into a definitive reference. Chelsea Publishing Company, founded in New York in 1944, specialized in bringing important European mathematical works to English-speaking audiences, and this 1953 translation made Bieberbach's conformal mapping theory accessible to a generation of American mathematicians and engineers at a time when complex analysis was central to advances in aerodynamics, electrical engineering, and theoretical physics.