Introduction; Part I. Preliminaries: 1. A computational approach to causality; 2. Networks: from structure to dynamics; 3. Information and computability theories; Part II. Theory and Methods: 4. Algorithmic information theory; 5. The coding theorem method (CTM); 6. The block decomposition method (BDM); 7. Graph and tensor complexity; 8. Algorithmic information dynamics (AID); Part III. Applications: 9. From theory to practice; 10. Algorithmic dynamics in artificial environments; 11. Applications to integer and behavioural sequences; 12. Applications to evolutionary biology; Postface; Appendix: Mutual and conditional BDM; Glossary.