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The aim of this book is to discuss the present situation of Lagrangian and Hamiltonian formalisms involving higher order derivatives. The achievements of differential geometry in formulating a more modern and powerful treatment of these theories is described and an extensive review of the development of these theories in classical language is also given.

Differential geometry. Global analysis --- Classical mechanics. Field theory --- Mechanics. --- Field theory (Physics) --- Lagrange equations. --- Hamilton-Jacobi equations. --- Geometry, Differential. --- Geometry, Differential --- Hamilton-Jacobi equations --- Lagrange equations --- Mechanics --- Champs, Théorie des (Physique) --- Géométrie différentielle --- Hamilton-Jacobi, Equations de --- Lagrange, Equations de --- Mécanique --- ELSEVIER-B EPUB-LIV-FT --- Field theory (Physics). --- Differential geometry --- Equations, Hamilton-Jacobi --- Equations, Jacobi-Hamilton --- Jacobi-Hamilton equations --- Calculus of variations --- Differential equations, Partial --- Hamiltonian systems --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Differential equations --- Equations of motion --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory