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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 specifically, in differential geometry a geodesic map (or geodesic mapping or geodesic diffeomorphism) is a function that "preserves geodesics". Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus, as well as linear and multilinear algebra, to study problems in geometry. The theory of plane and space curves and of surfaces in the three-dimensional Euclidean space formed the basis for its initial development in the eighteenth and nineteenth century. Since the late nineteenth century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds.