Approximately additive and approximately linear mappings; stability of the quadratic functional equation; generalizations - the method of invariant means; approximately multiplicative mappings - superstability; stability of functional equations for trigonometric and similar functions; functions with bounded nth differences; approximately convex functions; stability of the generalized orthogonality functional equation; stability and set-valued mappings; stability of stationary and minimum points; functional congruences; quasi-additive functions and related topics.