The authors first state the fundamental properties of bounded linear operators on a Hilbert space. Then they tell the history of the Kantorovich inequality, and describe how the Kantorovich inequality develops in the field of operator inequalities. The Mond- Pečarić method for convex functions has outlined a more complete picture of that inequality in the field of operator inequalities. The better part of the book is devoted to presenting many new results by using said method. In such context, the generalization and improvement of many famous inequalities are presented.