decade long experience of teaching the course \emph{Fundamental of Geometry} at the University of North Carolina at Charlotte, many notes for exercises, and reading and research are the bases for this bulky work.
The present third volume recalls Hilbert's axioms from the Foundations of Geometry,
and elaborates many faces of advanced neutral and Euclidean geometry. A first part about neutral geometry originates from the century long efforts to prove the parallel axiom, from Proclus in antiquity to Legendre and his contemporaries. The insight of independence of the parallel axiom leaves many open roads to pursue,
and the desire to develop a natural as well as completely axiomatic system still motivates new developments. The second part about advanced Euclidean geometry contains thorough triangle geometry, harmonic points, some elliptic geometry, and many more interesting problems.