Linear Differential Equations and Group Theory from Riemann to Poincare

This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry.The text for this second edition has been greatly expanded and revised, and the existing appendices enriched with historical accounts of the Riemann Hilbert problem, the uniformization theorem, Picard Vessiot theory, and the hypergeometric equation in higher dimensions. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.