This book develops the geometric intuition of the reader by
examining the symmetries (or rigid motions) of the space in
question. This approach introduces in turn all the classical
geometries: Euclidean, affine, elliptic, projective and hyperbolic.
The main focus is on the mathematically rich two-dimensional case,
although some aspects of 3- or $n$-dimensional geometries are
included. Basic notions of algebra and analysis are used to convey
better understanding of various concepts and results. Concepts of
geometry are presented in a very simple way, so that they become
easily accessible: the only pre-requisites are calculus, linear
algebra and basic analytic geometry.
General
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