Accessible‎,‎ concise‎,‎ and self‎-contained‎,‎ this book offers an outstanding introduction to three related subjects‎:‎ differential geometry‎,‎ differential topology‎,‎ and dynamical systems‎.‎ Topics of special interest addressed in the book include Brouwer‎'‎s fixed point theorem‎,‎ Morse Theory‎,‎ and the geodesic flow‎.‎ Smooth manifolds‎,‎ Riemannian metrics‎,‎ affine connections‎,‎ the curvature tensor‎,‎ differential forms‎,‎ and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics‎.‎ The authors also discuss the Gauss‎-Bonnet theorem and its implications in non‎-Euclidean geometry models‎.‎ The differential topology aspect of the book centers on classical‎,‎ transversality theory‎,‎ Sard‎'‎s theorem‎,‎ intersection theory‎,‎ and fixed‎-point theorems‎.‎ The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure‎.‎ It also furnishes some of the tools necessary for a complete understanding of the Morse theory‎.‎ These discussi‎.‎‎.‎‎.‎