Mathematical Methods of Analytical Mechanics uses tensor geometry and geometry of variation calculation, includes the properties associated with Noether's theorem, and highlights methods of integration, including Jacobi's method, which is deduced. In addition, the book covers the Maupertuis principle that looks at the conservation of energy of material systems and how it leads to quantum mechanics. Finally, the book deduces the various spaces underlying the analytical mechanics which lead to the Poisson algebra and the symplectic geometry. - Helps readers understand calculations surrounding the geometry of the tensor and the geometry of the calculation of the variation - Presents principles that correspond to the energy conservation of material systems - Defines the invariance properties associated with Noether's theorem - Discusses phase space and Liouville's theorem - Identifies small movements and different types of stabilities