This paper introduces the notation and ideas of modern Differential Geometry that form an essential background to many fields in Mathematics and Physics. It develops the theory of manifolds and bundles from a largely intuitive standpoint, and discusses the geometric notions of metric, connexion, geodesic, curvature and sectional curvature. Notes are supplied. The paper is an essential prerequisite for MATH 465. No more than two of MATH 464, MATH 465, MATH 466 and MATH 467 will be available in a year, to be decided by student request.
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