This book is an introduction to the study of fundamental inequalities like the arithmetic mean-geometric mean inequality, the Cauchy-Schwarz inequality, the Chebyshev inequality, the rearrangement inequality, inequalities for convex and concave functions. The emphasis is on the use of these inequalities for solving problems. Its special feature is a chapter on the geometrical inequalities which studies relations between various geometrical measures. It contains more than 300 problems, many of which are applications of inequalities. A large number of problems are taken from the International Mathematical Olympiads (IMO) and many national olympiads from countries across the world. The book will be very useful for students participating in mathematical contests. It should also help graduate students in consolidating their knowledge of inequalities by way of applications.