Jet bundles, geometric PDEs and calculus of variations

Jet bundles

Vinogradov, An informal introduction to the geometry of jet spaces

Saunders, The geometry of jet bundles

Geometric theory of PDEs

Arnold, Lectures on partial differential equations

Kruglikov and Lychagin, Geometry of differential equations

Bryant et al, Exterior differential systems

Eliashberg and Mishachev, Introduction to the h-principle

Gromov, Partial differential relations

Symmetries of ODEs and PDEs

The Sophus Lie e-library of the Diffiety Institute

Vinogradov, Local symmetries and conservation laws

Olver, Equivalence, invariants and symmetry

Olver, Applications of Lie groups to differential equations

Vinogradov et al, Symmetries and conservation laws for differential equations of mathematical physics

Vinogradov, Cohomological analysis of partial differential equations and secondary calculus

Nestruev, Smooth manifolds and observables

Calculus of variations

Krupka, Introduction to Global Variational Geometry

Gelfand & Fomin, Calculus of Variations

Giaquinta & Hildebrandt, Calculus of Variations, vol. I & II

Young, Lectures on the calculus of variations and optimal control theory

Struwe, Variational methods