This volume provides a study of some of the well-known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy--Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shannon's and related inequalities, generalised Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp-norm inequalities in convolutions, Heyers--Ulam stability of functional equations in connection with classical inequalities, inequalities for polynomial zeros, as well as applications in a number of problems of pure and applied mathematics.