Geometry and Topology Van Miles Reid and Balazs Szendroi is an English-language textbook that focuses on students and professionals in higher education. The book covers fundamental concepts of geometry and topology, with an emphasis on coordinate systems and symmetries.
The content ranges from Euclidean and non-Euclidean geometries, such as spherical and hyperbolic forms, to affine and projective linear geometries. Group theory is introduced to analyze geometric symmetries, leading to the connection between geometry and group theory within the Erlangen program. It also includes a basic introduction to topology, with examples such as the Möbius strip and the Klein bottle, to clarify quotient topologies and homeomorphisms.
The combination of topology and group theory opens up applications in relativity theory and quantum mechanics. With minimal prior knowledge, this reference work provides a first introduction to current research topics in algebra, geometry, and theoretical physics. The book includes numerous illustrations and concludes each chapter with extensive exercises. Additional teaching materials and assignments are available online for instructors.