This is a first textbook that is entirely focused on the up-to-date developments of null curves with their applications to science and engineering. It fills an important gap in a second-level course in differential geometry, as well as being essential for a core undergraduate course on Riemannian curves and surfaces. The sequence of chapters is arranged to provide in-depth understanding of a chapter and stimulate further interest in the next. The book comprises a large variety of solved examples and rigorous exercises that range from elementary to higher levels. This unique volume is self-contained and unified in presenting: a systematic account of all possible null curves, their Frenet equations, unique null Cartan curves in Lorentzian manifolds and their practical problems in science and engineering; and, the geometric and physical significance of null geodesics, mechanical systems involving curvature of null curves, simple variation problems and the interrelation of null curves with hypersurfaces.
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