Many problems in navigation which, because of the true shape of the Earth, seemed numerically and algebraically impractical, can now be resolved by computers. Nevertheless, traditional methods provide important back-up, for which geometry is invaluable. This book offers a treatment of the Earth as an ellipsoid of revolution, pictured as a sphere, as has served navigators for centuries and applies to surface navigation and also to the surfaces of planets. It also includes methods for fixing a position by astronomical observation, as well as from the tracking of the angular co-ordinates of an astronomical body.