Whereas numerous tomes of comprehensive studies of navigation and related subjects are readily available for the professional navigator, there is dearth of publications suitable for the amateur navigator in a how-to form. Furthermore, the appearance of relatively inexpensive electronic devices, such as the GPS, has lured would-be navigators away from the traditional methods of navigation, in spite of the warnings offered by the companies producing these devices. Thus they overlook the sine qua non of good navigation, the determination of the current velocity, that is the set and drift. Once determined this component of the navigational triangle makes precise navigation a snap, whereas without it there is only uncertainty. of basic formulae employing basic trigonometry and later spherical trigonometry, methods which have evolved over the centuries from the beginning of the Age of Exploration in the early 1400's to modern days. In this text we develop the knowledge and application of these mathematical processes in such a way as to reassure the student that these techniques are not beyond his capabilities.