Preface At the Beginning Diffeology, the Axiomatic The Irrational Tori 8 Generating Families, Dimension Cartan-De-Rham Calculus Diffeology Fiber Bundles Homotopy Theory in Diffeology Local Diffeology, Modeling Modeling: Manifolds, Orbifolds and Quasifolds Symplectic Mechanics and Diffeology Diffeology and Non-Commutative Geometry Functional Diffeology on Fourier Coefffcients Smooth Function on Periodic Functions Symplectic Diffeology on Smooth Periodic Functions Infinite Torus Action on Smooth Periodic Functions Basic 1-Forms on Principal Fiber Bundles Differential of Holonomy for Torus Bundles Non-symplectic manifold with injective univ. moment map On Riemannian Metric in Diffeology A Few Half-Lines 1-Forms on Half-Lines 1-Forms on the Subset Half-Line Cotangent Space of the Half-Line 1-Forms on Half-Spaces p-Forms on Half-Spaces p-Forms on Corners Differential Forms on the Cross A note on Hamiltonian Diffeomorphisms Differential of a Lie-Group Valued Function The Geodesics of the 2-Torus The Use of the Moment Map in Geodesic Calculus The Parasymplectic Space of Geodesics Trajectories Diffeomorphisms of Geod(T2) The Diffeomorphisms of the Square Diffeological Spaces are Locally Connected Vague Adjunction of a Point to a Space Embedding a Diffeological Space Into its Powerset Foliations and Diffeology Klein Stratiffcation of Diffeological Spaces Lagrange’s Equations of Motion Poisson Bracket in Diffeology Smooth embeddings and smoothly embedded subsets Seifert Orbifolds Symplectic spaces without Hamiltonian diffeomorphisms The Diffeology Framework of General Covariance Postface: The Beginning of Diffeological Spaces Appendix: A Categorical Approach to Diffeology Bibliography
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