The subject of inequalities provides a rich source of material for mathematics competitions and beyond. This accessible text aims to give the enthusiastic student plenty of tips on how to select the correct sort of inequality and how to apply it effectively to a given problem. It is a thoroughly revised and extended edition of a book initially published as part of the composite volume ‘Introductions to Number Theory and Inequalities’. The author was an Oxford University lecturer and teacher at Clifton College, Bristol. For ages 16+ competition preparation.