An almost completely decomposable abelian (acd) group is an extension of a finite direct sum of subgroups of the additive group of rational numbers by a finite abelian group. Examples are easy to write and are frequently used but have been notoriously difficult to study and classify because of their computational nature. However, a general theory o

1. Notation and Background 2. Basics and Completely Decomposable Groups 3. Cyclic Essential Extensions 4. Regulating Subgroups and Regulators 5. Local-Global Relationships 6. Groups with Cyclic Regulating 7. Completely Decomposable Summands 8. Anti-Representations 8. Near-Isomorphism and Type-Isomorphism 9. Fundamental Decomposition Theorems 10. Finite Essential Extensions 11. Representing Matrices 12. Classification 13. Direct Decompositions of Block-Rigid crq-Groups 14. In Search for Good Categories 15. Associated Structures 16. Literature