William M. Goldman, University of Maryland, College Park, MD.

• Part 1. Affine and projective geometry: Affine geometryProjective geometryDuality and non-Euclidean geometryConvexityPart 2. Geometric manifolds: Locally homogeneous geometric structuresExamples of geometric structuresClassificationCompletenessPart 3. Affine and projective structures: Affine structures on surfaces and the Euler characteristicAffine Lie groupsParallel volume and completenessHyperbolicityProjective structures on surfacesComplex-projective structuresGeometric structures on 3-manifoldsAppendices: Appendix A. Transformation groupsAppendix B. Affine connectionsAppendix C. Representations of nilpotent groupsAppendix D. 4-dimensional filiform nilpotent Lie algebrasAppendix E. Semicontinuous functionsAppendix F. $\mathsf{SL}(2,\mathbb{C})$ and $O(3,1)$Appendix G. Lagrangian foliations of symplectic manifoldsBibliographyIndex

William M. Goldman, University of Maryland, College Park, MD.

• Part 1. Affine and projective geometry: Affine geometryProjective geometryDuality and non-Euclidean geometryConvexityPart 2. Geometric manifolds: Locally homogeneous geometric structuresExamples of geometric structuresClassificationCompletenessPart 3. Affine and projective structures: Affine structures on surfaces and the Euler characteristicAffine Lie groupsParallel volume and completenessHyperbolicityProjective structures on surfacesComplex-projective structuresGeometric structures on 3-manifoldsAppendices: Appendix A. Transformation groupsAppendix B. Affine connectionsAppendix C. Representations of nilpotent groupsAppendix D. 4-dimensional filiform nilpotent Lie algebrasAppendix E. Semicontinuous functionsAppendix F. $\mathsf{SL}(2,\mathbb{C})$ and $O(3,1)$Appendix G. Lagrangian foliations of symplectic manifoldsBibliographyIndex