A decade long experience of teaching the course Fundamental of Geometry at the University of North Carolina at Charlotte, many notes for exercises, reading and research are the bases for this bulky work. The present first volume begins with Hilbert’s axioms from the Foundations of Geometry. After some discussion of logic and axioms in general, we go on with a short section about incidence geometries in two and three dimensions. As in Hilbert’s system, there follow detailed sections about the axioms of order, next about congruence in neutral geometry, -which means without assumption of the axiom of parallelism. I deal with the axioms of measurement and of completeness, and deviating from Hilbert, with axioms about circles. The last two sections deal with the theory of area in neutral geometry, and neutral triangle geometry. My heartfelt thanks go to everyone involved, this means famous authors as well as my former students.