It is certainly true that the concept of information is one of the dominant ideas of the second half of the twentieth century. People from all walks of life are concerned with information processing. Many of the inventions of the current era deal with storage, transmission, transformation and retrieval of information. Information can be manifested however in various forms, for example orally, in writing, electronically, etc. From mathematical point of view, the essence of information is its quantity, and the basic problem is how to measure information quantity. Commonly it is done by introducing desirable properties for an information measure, then using those properties to determine explicit forms for information measures. While doing this we rely heavily upon the theory of functional equations. The book deals with the stability problem of some functional equations that appear in the characterization problem of information measures.