Gray J.J. Linear Differential Equations and Group Theory from Riemann to Poincare

Birkhauser, 2000. - 338 pages.
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 new edition has been greatly expanded and revised, and the existing appendices enriched with historical accounts of the Riemann-Hilbert problem, the unformization 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.
This work continues to be the only up-to-date scholarly account of the history of a branch of mathematics that continues to generate important research, for which the mathematics has been the occasion for some of the most profound work by numbers 19th century figures: Riemann, Fuchs, Dedekind, Klein, and Poincaré.