The aim of this volume is to introduce and exchange recent new topics in the areas of probability theory and applications in inequality theory, stochastic analysis and applications. Contents: Preface; Aczel's Inequality, Superadditivity and Horistology; Some Inequalities for the Integral Mean of Holder Continuous Functions Defined on Disks in a Plane; Ostrowski Type Inequalities for Functions whose Modulus of the Derivatives are Convex and Applications; Generalised Taylor's Formula with Estimates of the Remainder; Three-Point Rules and Applications for Absolutely Continuous Functions; On Parallelogram Law and Bohr's Inequality in n-Inner Product Spaces; An Integral Inequality Related to the Ostrowski Result and Applications; On Some Variants of Jensen's Inequality; Proofs of Wilker's Inequalities Involving Trigonometric Functions; Some Osrowski Type Inequalities for Double Integrals if Functions whose Partial Derivatives Satisfy Certain Convexity Properties; On the Mappings of Conservative Distances; A New Analogue Gauss' Functional Equations and Characterizations of Integral Mean Values; Moments Inequalities of a Random Variable Defined over a Finite Interval; On Norm Inequalities