1. Geometric foundations; 2. Lie groups; 3. Representation theory; 4. Jets and contact transformations; 5. Differential invariants; 6. Symmetries of differential equations; 7. Symmetries of variational problems; 8. Equivalence of coframes; 9. Formulation of equivalence problems; 10. Cartan's equivalence method; 11. Involution; 12. Prolongation of equivalence problems; 13. Differential systems; 14. Frobenius' theorem; 15. The Cartan–Kahler existence theorem.
Presents an innovative synthesis of methods used to study problems of equivalence and symmetry.
"...represents an important effort to present the theory of the equivalence problem in a modern language with many new applications to concrete situations; in the author's words, 'it is a provocative blend of mathematical flavors'. Most of the material is of interest, and easily readable, for a wide class of specialists in different areas, as the book offers applications ranging over a great variety of fields." Jaime Munoz Masque, Mathematical Reviews "Olver's highly original exposition gives a unified approach to a wide variety of problems of this sort via Cartan's equivalence method...this well-written book will interest a wide variety of mathematicians and graduate students." D.V. Feldman, Choice
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