Synopsis
This is a thorough analysis of the fundamentals of plane geometry - Euclidean, spherical and projective. The reader is provided with an abundance of geometrical facts such as classical results of plane Euclidean and non-Euclidean geometry investigation of conic sections, projective spaces, Galilean transformations, Lorentz transformations, and Minkowskii geometry. The author considers a range of interesting problems which one meets in real life - the number of images one sees in a pair of mirrors, how to detect the position of an enemy ship from two different listening posts and the distance between two cities knowing their latitude and longitude.
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