In this volume algorithms are compared for rhumb line sailing (RLS) and great elliptic sailing (GES) calculations commonly used for route planning and route monitoring. Compact vector formulas are given for the great circle and rhumb line on the sphere and rhumb line, great circle, great ellipse and geodesic line on the spheroid providing vector solutions to both the forward and the inverse problems and conversions of longitude and latitude. The solution incorporates a closed form for the azimuth and the derivation of this equation is presented and illustrated. This handbook also shows that a computer algebra system and linear algebra are powerful tools to solve some mathematical derivations that may be useful in navigation, geodesy, and cartography.The book demonstrates the manufacturers of ECDIS systems and GNSS receivers a wide spectrum of solutions possible to use in their algorithms from very simple (on the flat or on the sphere) to very complicated (on the surface of ellipsoid).