Thisbookgivesthebasicnotionsofdifferentialgeometry,suchasthemetrictensor,theRiemanncurvaturetensor,thefundamentalformsofasurface,covariantderivatives,andthefundamentaltheoremofsurfacetheoryinaself-containedandaccessiblemanner.Althoughthefieldisoftenconsidereda"classical"one,ithasrecentlybeenrejuvenated,thankstothemanifoldapplicationswhereitplaysanessentialrole.Thebookpresentssomeimportantapplicationstoshells,suchasthetheoryoflinearlyandnonlinearlyelasticshells,theimplementationofnumericalmethodsforshells,andmeshgenerationinfiniteelementmethods.Thisvolumewillbeveryusefultograduatestudentsandresearchersinpureandappliedmathematics.