Reading Guide
One of the most comprehensive introductory surveys of the subject, charting the historical development from before Gauss to modern times, is by Berger (2004). Accounts of the classical theory are given in Eisenhart (2004), Kreyszig (1991) and Struik (1988); the more modern copiously illustrated undergraduate textbooks by Gray, Abbena & Salamon (2006), Pressley (2001) and Wilson (2008) might be found more accessible. An accessible account of the classical theory can be found in Hilbert & Cohn-Vossen (1952). More sophisticated graduate-level treatments using the Riemannian connection on a surface can be found in Singer & Thorpe (1967), do Carmo (1976) and O'Neill (1997).
Read more about this topic: Differential Geometry Of Surfaces
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