The book describes Fluid Dynamics, Magnetohydrodynamics, and Classical Thermodynamics as branches of Lagranges Analytical Mechanics; and in that sense, the approach presented in it is markedly different from the treatment given to them in traditional text books. A Hamilton-Type Variational Principle as the proper mathematical technique for the theoretical description of the dynamic state of any fluid is formulated. The scheme is completed proposing a new group of variations regarding the evolution parameter which is time; and with the demonstration of a theorem concerning the invariance of the action integral under continuous and infinitesimal temporary transformations. A general methodology for the mathematical treatment of fluid flows characteristic of Fluid Dynamics, Magnetohydrodynamics, and also fluids at rest proper of Classical Thermodynamics is presented. The volume contains the most significant results obtained by the author in Continuous Mechanics and Astrophysics.