Preface 1. Types of convergence 2. Martingale convergence theorems 3. Sub- and supermartingale convergence theorems 4. Basic inequalities for adapted sequences 5. Convergence of generalized martingales in Banach spaces - the mean way 6. General directed index sets and applications of amart theory 7. Disadvantages of amarts: convergence of generalized martingales in Banach spaces - the pointwise way 8. Convergence of generalized sub- and supermartingales in Banach lattices 9. Closing remarks References List of notations Subject index.