This tutorial text and problem collection is designed to introduce the student, at undergraduate or senior high school level, to the elementary properties of inequalities. A knowledge of algebra, geometry and trigonometry, together with a first course in calculus, provides a sufficient background for almost all the material. It is hoped that, as a collection of problems, the book will be a useful adjunct to regular course work, while the provision of an introductory survey and numerous complete solutions will give students an opportunity for independent study.