By Shiing-Shen Chern, Wei-Huan Chen, K. S. Lam

This publication is a translation of an authoritative introductory textual content in keeping with a lecture sequence introduced by way of the well known differential geometer, Professor S S Chern in Beijing collage in 1980. the unique chinese language textual content, authored by means of Professor Chern and Professor Wei-Huan Chen, was once a different contribution to the math literature, combining simplicity and economic system of process with intensity of contents. the current translation is geared toward a large viewers, together with (but no longer restricted to) complicated undergraduate and graduate scholars in arithmetic, in addition to physicists attracted to the various purposes of differential geometry to physics. as well as a radical remedy of the basics of manifold thought, external algebra, the outside calculus, connections on fiber bundles, Riemannian geometry, Lie teams and relocating frames, and complicated manifolds (with a succinct creation to the speculation of Chern classes), and an appendix at the dating among differential geometry and theoretical physics, this e-book incorporates a new bankruptcy on Finsler geometry and a brand new appendix at the heritage and up to date advancements of differential geometry, the latter ready especially for this variation by means of Professor Chern to convey the textual content into views.