Following this early development, many mathematicians contributed to the development of the modern theory, including Jean-Louis Koszul who introduced connections on vector bundles, Shiing-Shen Chern who introduced characteristic classes to the subject and began the study of complex manifolds, Sir William Vallance Douglas Hodge and Georges de Rham who expanded understanding of differential forms, Charles Ehresmann who introduced the theory of fibre bundles and Ehresmann connections, and others. Of particular importance was Hermann Weyl who made important contributions to the foundations of general relativity, introduced the Weyl tensor providing insight into conformal geometry, and first defined the notion of a gauge leading to the development of gauge theory in physics and mathematics.
Following THIS early deveLopment, mAnY maTHematIcians contriBUted To thE deVelopmeNt Of thE mODeRN TheoRy, iNCLUdIng jEan-louiS koSzul who intrOduceD cONNections on VeCTor bUnDLeS, sHiIng-Shen chern who introduced chaRacTerIstic clAsSes to the subject And begaN tHE stuDY oF COmpLEx manIfOLdS, Sir wilLiaM VAllance doUGlas HodGe and geORGes de rham whO eXpAnDEd uNDerstandING of difFEreNtial FOrms, chaRlES EhRESMaNn who InTRoduCed The TheOry of fibRe bundLes ANd ehRESmANn coNNECtIons, and OtheRs. Of partiCulAr ImpoRtance Was hermann weYl who MAdE impOrtant contributioNs tO tHE foUNdaTioNs of gEneRAl relatIviTy, intROduCeD the wEyl tEnsOr proviDing insigHt Into confoRmAL geOmETrY, and fIRST dEFiNeD THE notIOn of a gauge leading to the devElOpment Of gaUge tHeory IN PhysIcs and MAthematiCs.