This tract sets out to give some idea of the basic techniques and of some of the most striking results of Diophantine approximation. A selection of theorems with complete proofs are presented, and Cassels also provides a precise introduction to each chapter, and appendices detailing what is needed from the geometry of numbers and linear algebra. Some chapters require knowledge of elements of Lebesgue theory and algebraic number theory. This is a valuable and concise text aimed at the final-year undergraduate and first-year graduate student.