Geometry offers an entire diversity of perspectives at the universe, serving because the thought, technical toolkit and supreme objective for lots of branches of arithmetic and physics. This e-book introduces the information of geometry, and encompasses a beneficiant offer of straightforward factors and examples. The remedy emphasises coordinate platforms and the coordinate adjustments that generate symmetries. The dialogue strikes from Euclidean to non-Euclidean geometries, together with round and hyperbolic geometry, after which directly to affine and projective linear geometries. crew idea is brought to regard geometric symmetries, resulting in the unification of geometry and team conception within the Erlangen software. An creation to simple topology follows, with the Möbius strip, the Klein bottle and the skin with g handles exemplifying quotient topologies and the homeomorphism challenge. Topology combines with team thought to yield the geometry of transformation groups,having functions to relativity idea and quantum mechanics. a last bankruptcy gains old discussions and symptoms for extra studying. With minimum must haves, the ebook presents a primary glimpse of many learn themes in sleek algebra, geometry and theoretical physics. The publication relies on decades' educating event, and is carefully class-tested. There are copious illustrations, and every bankruptcy ends with a large offer of workouts. extra instructing fabric is offered for academics through the internet, together with assignable challenge sheets with solutions.