This book addresses essential foundations of Euclidean geometry as well as several non-Euclidean geometries, thereby supporting students of mathematics, physics, astronomy, geography, geodesy, and navigation. The diverse connections between selected topics in Euclidean geometry, taxi geometry, projective, spherical, and hyperbolic geometry also benefit students in mathematics education. It particularly facilitates the understanding of issues related to synthetic geometry, special and general relativity, astrometry, map design, and navigation. Characteristic features of this book include its connection to school-level knowledge and the clarification of concepts and methods through comprehension-enhancing background information, numerous illustrations, thoroughly worked-out examples, and detailed descriptions.