Differential Geometry

1. Read each chapter's introduction first to clarify what geometric problem the chapter addresses, then move on to definitions and theorems
2. Keep paper and pen ready to re-derive key theorems section by section, understanding quantities such as curvature and torsion in relation to figures
3. After each chapter, complete the exercises independently and check wrong answers against the corresponding definitions rather than rushing to solutions
4. When reading alongside a manifolds or Riemannian geometry textbook, record the correspondence between classical results and general theory

Peking University Press is a comprehensive university press whose publishing areas cover classical literature, popular science, social culture, world history, Western philosophy, and culture. Its catalogue contains 6,031 titles, with representative books including A Dream of Red Mansions, Relativity: The Special and General Theory (15th Edition) (with Einstein's classic papers on unified field theory and other topics), Elements, Conics, The Aristocratic Families of the Eastern Jin, The Philosophy of Mythology (Volume I), The Philosophy of Mythology (Volume II), and The Origin of Continents and Oceans. Representative authors include Cao Xueqin, Zhou Ruchang, Albert Einstein, Euclid, Apollonius, Tian Yuqing, Schelling, and Xian Gang. The press has developed distinctive strengths in classical Chinese literature and in the translation of Western philosophical classics, while also covering scientific classics and social and cultural studies. As public information is limited, this description is based only on the books in the catalogue and offers no further extrapolation.