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