This book reports on the new results in Abstract Systems Theory (AST). It shows the progress made so far in the effort launched in 1960 to develop a mathematical theory of systems based on the top-down-formalization-approach. The volume can be used as a supplementary reading in courses in systems theory and engineering. The material is organized in such a way that portions of the book relevant for the supplementary reading in different courses can be used independently from the rest of the text.