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This Book Makes A Systematic Study Of The Relations Between The étale Cohomology Of A Scheme And The Orderings Of Its Residue Fields. A Major Result Is That In High Degrees, étale Cohomology Is Cohomology Of The Real Spectrum. It Also Contains New Contributions In Group Cohomology And In Topos Theory. It Is Of Interest To Graduate Students And Researchers Who Work In Algebraic Geometry (not Only Real) And Have Some Familiarity With The Basics Of étale Cohomology And Grothendieck Sites. Independently, It Is Of Interest To People Working In The Cohomology Theory Of Groups Or In Topos Theory. Contents: Part One: Real Spectrum And Real étale Site -- Glueing étale And Real étale Site -- Limit Theorems, Stalks, And Other Basic Facts -- Some Reminders On Weil Restrictions -- Real Spectrum Of X And étale Site Of X - Ä -1Ü -- The Fundamental Long Exact Sequence, Cohomological Dimension Of Xb,i: Reduction To The Field Case -- Equivariant Sheaves For Actions Of Topological Groups -- Cohomological Dimension Of Xb,ii: The Field Case. Part Two: G-toposes -- Inverse Limits Of G-toposes: Two Examples -- High Degree Cohomology Of Profinite Groups -- Group Actions On Spaces: Topological Versus Topos-theoretic Constructions -- Quotient Topos Of A G-topos For G Of Prime Order. Part Three: Comparison Theorems -- Base Change Theorems -- Constructible Sheaves And Finiteness Theorems -- Cohomology Of Affine Varieties -- Relations To The Zariski Topology -- Examples And Complements. Claus Scheiderer. Includes Bibliographical References And Index. This book makes a systematic study of the relations between the etale cohomology of a scheme and the orderings of its residue fields. A major result is that in high degrees, etale cohomology is cohomology of the real spectrum. Independently, it is of interest to people working in the cohomology theory of groups or in topos theory.