This book provides a systematic treatment of the main results on the Morse index of minimal submanifolds of Riemannian manifolds. After an introductory chapter reviewing the necessary material, this book provides a survey of the basic properties of the Morse index, as well as a large number of examples of minimal submanifolds with the corresponding calculation of their Morse index. The analysis of minimal submanifolds and their index in the cases when the ambient manifold is the Euclidean space, sphere, real and complex projective spaces are analyzed in detail; many other classes of ambient varieties are also studied. The text also includes some of the main open problems in the theory. Potential readers of this book are graduate students and researchers in geometric analysis. This book is published in cooperation with Real Sociedad Matematica Espanola.