Arielle Leitner is a research consultant at the Weizmann Institute of Science, and a lecturer at the Afeka College of Engineering. She earned her PhD in 2015 from the University of California, Santa Barbara, and held postdocs at the Technion and at Weizmann before joining Afeka. Her research concerns the interplay between low-dimensional topology, geometry, dynamics, and algebra.Federico Vigolo studied mathematics at the Scuola Normale Superiore di Pisa and completed his doctorate at the University of Oxford in 2018. He held postdoctoral positions at the Weizmann Institute of Science and the University of Münster before being appointed Junior Professor at the University of Göttingen in 2022. He is especially interested in large scale geometry and the interactions between coarse geometric techniques and other subjects, most notably in analysis, algebra and dynamical systems.

• - 1. Introduction. - Part I Basic Theory. - 2. Introduction to the Coarse Category. - 3. Properties of the Category of Coarse Spaces. - 4. Coarse Groups. - 5. Coarse Homomorphisms, Subgroups and Quotients. - 6. Coarse Actions. - 7. Coarse Kernels. - Part II Selected Topics. - 8. Coarse Structures on Set-Groups. - 9. Coarse Structures on Z. - 10. On Bi-Invariant Word Metrics. - 11. A Quest for Coarse Groups that are not Coarsified Set-Groups. - 12. On Coarse Homomorphisms and Coarse Automorphisms. - 13. Spaces of Controlled Maps.

Arielle Leitner is a research consultant at the Weizmann Institute of Science, and a lecturer at the Afeka College of Engineering. She earned her PhD in 2015 from the University of California, Santa Barbara, and held postdocs at the Technion and at Weizmann before joining Afeka. Her research concerns the interplay between low-dimensional topology, geometry, dynamics, and algebra.Federico Vigolo studied mathematics at the Scuola Normale Superiore di Pisa and completed his doctorate at the University of Oxford in 2018. He held postdoctoral positions at the Weizmann Institute of Science and the University of Münster before being appointed Junior Professor at the University of Göttingen in 2022. He is especially interested in large scale geometry and the interactions between coarse geometric techniques and other subjects, most notably in analysis, algebra and dynamical systems.

• - 1. Introduction. - Part I Basic Theory. - 2. Introduction to the Coarse Category. - 3. Properties of the Category of Coarse Spaces. - 4. Coarse Groups. - 5. Coarse Homomorphisms, Subgroups and Quotients. - 6. Coarse Actions. - 7. Coarse Kernels. - Part II Selected Topics. - 8. Coarse Structures on Set-Groups. - 9. Coarse Structures on Z. - 10. On Bi-Invariant Word Metrics. - 11. A Quest for Coarse Groups that are not Coarsified Set-Groups. - 12. On Coarse Homomorphisms and Coarse Automorphisms. - 13. Spaces of Controlled Maps.

Arielle Leitner is a research consultant at the Weizmann Institute of Science, and a lecturer at the Afeka College of Engineering. She earned her PhD in 2015 from the University of California, Santa Barbara, and held postdocs at the Technion and at Weizmann before joining Afeka. Her research concerns the interplay between low-dimensional topology, geometry, dynamics, and algebra.Federico Vigolo studied mathematics at the Scuola Normale Superiore di Pisa and completed his doctorate at the University of Oxford in 2018. He held postdoctoral positions at the Weizmann Institute of Science and the University of Münster before being appointed Junior Professor at the University of Göttingen in 2022. He is especially interested in large scale geometry and the interactions between coarse geometric techniques and other subjects, most notably in analysis, algebra and dynamical systems.

• - 1. Introduction. - Part I Basic Theory. - 2. Introduction to the Coarse Category. - 3. Properties of the Category of Coarse Spaces. - 4. Coarse Groups. - 5. Coarse Homomorphisms, Subgroups and Quotients. - 6. Coarse Actions. - 7. Coarse Kernels. - Part II Selected Topics. - 8. Coarse Structures on Set-Groups. - 9. Coarse Structures on Z. - 10. On Bi-Invariant Word Metrics. - 11. A Quest for Coarse Groups that are not Coarsified Set-Groups. - 12. On Coarse Homomorphisms and Coarse Automorphisms. - 13. Spaces of Controlled Maps.