Smooth Quasigroups and Loops

Preface. Introduction. 0. Introductory Survey: Quasigroups, Loopuscular Geometry and Nonlinear Geometric Algebra. Part One: Fundamental Structures of Nonlinear Geometric Algebra. 1. Basic Algebraic Structures. 2. Semidirect Products of a Quasigroup by its Transassociants. 3. Basic Smooth Structures. Part Two: Smooth Loops and Hyperalgebras. 4. Infinitesimal Theory of Smooth Loops. 5. Smooth Bol Loops and Bol Algebras. 6. Smooth Moufang Loops and Mal'Cev Algebras. 7. Smooth Hyporeductive and Pseudoreductive Loops. Part Three: Loopuscular Geometry. 8. Affine Connections and Loopuscular Structures. 9. Reductive Geoodular Spaces. 10. Symmetric Geoodular Spaces. 11. s-Paces. 12. Geometry of Smooth Bol and Moufang Loops. Appendices. Bibliography. Index.