One of the biggest difficulties in astronomy is establishing the limits of observational errors in order to avoid inadequate or incorrect interpretation of data. This requires a thorough understanding of the methods used by astronomers used to calculate distances, diameters, temperatures ages and other parameters and an ability to assess their reliability. Such methods range from the simplest techniques, which have been used since ancient times, to extremely sophisticated computer based techniques. Both have their uses, and the simple methods are still used today to give a first approximation. The purpose of this book is to explain some of these methods by example and then to give the reader further practice by the use of problems. The first section of the book is concerned with aspects of fundamental astronomy: the position and movement of a body on the celestial sphere and the effects of the Earth's motions. The second and third sections are concerned with ancient and modern methods for determining the distances, trajectories, sizes, features, masses, luminosities, temperatures, chemical compositions, ages and similar parameters within the solar system and nearby stars. Extra-galactic astronomy is dealt with in the fourth and final section.