This book is intended as a text and reference both in some basic theoretical topics of proba-bility theory and some topics able to suggest re-searches regarding the convergence and approxi-mation in the study of systems. It is written especially from a practical po-int of view, based on main theoretical results. It appears as a special field with a profound pragmatic character. To be accessible to as great a number as possible of readers, a methodical and gradual introduction in the problems is made. Various examples and applications illustrate the questions discussed. Also a wide references is given at the end of the book. In this sense the book can become useful to all those who are interested in problems of mo-delling certain scientific phenomena they are concerned with. The book also contains the essential material for an introductory course (senior or first-year graduate level) for students in mathematics and statistics, in mechanics and electrical engi-neering or in economical, financial, biological or social sciences as well as for research workers in the large variety of applied fields.