This two-volume set collects and presents many fundamentals of mathematics in an enjoyable and elaborating fashion. The idea behind the two books is to provide substantials for assessing more modern developments in mathematics and to present impressions which indicate that mathematics is a fascinating subject with many ties between the diverse mathematical disciplines. The present volume examines many of the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history. Contents Geometry and geometric ideas Isometries in Euclidean vector spaces and their classification in n The conic sections in the Euclidean plane Special groups of planar isometries Graph theory and platonic solids Linear fractional transformation and planar hyperbolic geometry Combinatorics and combinatorial problems Finite probability theory and Bayesian analysis Boolean lattices, Boolean algebras and Stone’s theorem