Peter Schenzel retired from Martin Luther University Halle-Wittenberg in 2015. There, he gained his PhD in 1975, under the supervision of Wolfgang Vogel and his Habilitation in 1979. The latter was published in the Springer Lecture Notes in Mathematics. He published further more than 90 research papers. He was invited and speaker of several international conferences. For three years he was a member of the Max Planck Institute for Mathematics.Anne Marie Simon is professor at the Free University of Brussels. She received her PhD, under the guidance of Jacques Tits at the same university in 1969. She was a visitor at Brown University for one year. She published more than 20 research papers. At least two of them dealt with the study of completion and local homology and have been quoted in several research papers.

• Part I: Modules,- 1. Preliminaries and auxiliary results.- 2. Adic topology and completion.- 3. Ext-Tor vanishing and completeness criteria.- PartII: Complexes.- 4. Homological Preliminaries.- 5. Koszul complexes, depth and codepth.- 6. Čech complexes, Čech homology and cohomology.- 7. Local cohomology and local homology.- 8. The formal power series Koszul complex.- 9. Complements and Applications.- Part III: Duality.- 10. Čech and local duality.- 11. Dualizing complexes.- 12. Local duality with dualizing complexes and other dualities.- Appendix.- References.- Notation.- Subject Index.

Peter Schenzel retired from Martin Luther University Halle-Wittenberg in 2015. There, he gained his PhD in 1975, under the supervision of Wolfgang Vogel and his Habilitation in 1979. The latter was published in the Springer Lecture Notes in Mathematics. He published further more than 90 research papers. He was invited and speaker of several international conferences. For three years he was a member of the Max Planck Institute for Mathematics.Anne Marie Simon is professor at the Free University of Brussels. She received her PhD, under the guidance of Jacques Tits at the same university in 1969. She was a visitor at Brown University for one year. She published more than 20 research papers. At least two of them dealt with the study of completion and local homology and have been quoted in several research papers.

• Part I: Modules,- 1. Preliminaries and auxiliary results.- 2. Adic topology and completion.- 3. Ext-Tor vanishing and completeness criteria.- PartII: Complexes.- 4. Homological Preliminaries.- 5. Koszul complexes, depth and codepth.- 6. Čech complexes, Čech homology and cohomology.- 7. Local cohomology and local homology.- 8. The formal power series Koszul complex.- 9. Complements and Applications.- Part III: Duality.- 10. Čech and local duality.- 11. Dualizing complexes.- 12. Local duality with dualizing complexes and other dualities.- Appendix.- References.- Notation.- Subject Index.

Peter Schenzel retired from Martin Luther University Halle-Wittenberg in 2015. There, he gained his PhD in 1975, under the supervision of Wolfgang Vogel and his Habilitation in 1979. The latter was published in the Springer Lecture Notes in Mathematics. He published further more than 90 research papers. He was invited and speaker of several international conferences. For three years he was a member of the Max Planck Institute for Mathematics.Anne Marie Simon is professor at the Free University of Brussels. She received her PhD, under the guidance of Jacques Tits at the same university in 1969. She was a visitor at Brown University for one year. She published more than 20 research papers. At least two of them dealt with the study of completion and local homology and have been quoted in several research papers.

• Part I: Modules,- 1. Preliminaries and auxiliary results.- 2. Adic topology and completion.- 3. Ext-Tor vanishing and completeness criteria.- PartII: Complexes.- 4. Homological Preliminaries.- 5. Koszul complexes, depth and codepth.- 6. Čech complexes, Čech homology and cohomology.- 7. Local cohomology and local homology.- 8. The formal power series Koszul complex.- 9. Complements and Applications.- Part III: Duality.- 10. Čech and local duality.- 11. Dualizing complexes.- 12. Local duality with dualizing complexes and other dualities.- Appendix.- References.- Notation.- Subject Index.