Mikhail Borovoi, Tel Aviv University, Israel. Tasho Kaletha, University of Michigan, Ann Arbor, Michigan. Vladimir Hinich, University of Haifa, Israel

• Chapters; 1. Introduction; 2. Tate cohomology of bounded complexes; 3. The Tate-Nakayama isomorphism for bounded complexes of tori; 4. Absolute Galois cohomology in a special case; 5. Galois cohomology of reductive groups; 6. Explicit computations of Galois cohomology; 7. Computations with Tate-Shafarevich kernels; A. A long exact sequence containing $B_{ {\Gamma }\kern -0.8pt,Tors}$; B. $H^1$ for a crossed module; C. Duality; D. Fiber product; E. Cheat sheet on Tate cohomology

Mikhail Borovoi, Tel Aviv University, Israel. Tasho Kaletha, University of Michigan, Ann Arbor, Michigan. Vladimir Hinich, University of Haifa, Israel

• Chapters; 1. Introduction; 2. Tate cohomology of bounded complexes; 3. The Tate-Nakayama isomorphism for bounded complexes of tori; 4. Absolute Galois cohomology in a special case; 5. Galois cohomology of reductive groups; 6. Explicit computations of Galois cohomology; 7. Computations with Tate-Shafarevich kernels; A. A long exact sequence containing $B_{ {\Gamma }\kern -0.8pt,Tors}$; B. $H^1$ for a crossed module; C. Duality; D. Fiber product; E. Cheat sheet on Tate cohomology

Mikhail Borovoi, Tel Aviv University, Israel. Tasho Kaletha, University of Michigan, Ann Arbor, Michigan. Vladimir Hinich, University of Haifa, Israel

• Chapters; 1. Introduction; 2. Tate cohomology of bounded complexes; 3. The Tate-Nakayama isomorphism for bounded complexes of tori; 4. Absolute Galois cohomology in a special case; 5. Galois cohomology of reductive groups; 6. Explicit computations of Galois cohomology; 7. Computations with Tate-Shafarevich kernels; A. A long exact sequence containing $B_{ {\Gamma }\kern -0.8pt,Tors}$; B. $H^1$ for a crossed module; C. Duality; D. Fiber product; E. Cheat sheet on Tate cohomology