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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, projective differential geometry is the study of differential geometry, from the point of view of properties that are invariant under the projective group. This is a mixture of attitudes from Riemannian geometry, and the Erlangen program. The area was much studied by mathematicians from around 1890 for a generation (by J. G. Darboux, George Henri Halphen, Ernest Julius Wilczynski, E. Bompiani, G. Fubini, Eduard ech, amongst others), without a comprehensive theory of differential invariants emerging. Élie Cartan formulated the idea of a general projective connection, as part of his method of moving frames; abstractly speaking, this is the level of generality at which the Erlangen program can be reconciled with differential geometry, while it also develops the oldest part of the theory (for the projective line), namely the Schwarzian derivative.