• 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.

'... contains so much useful information ... I am sure that the book will fulfil its author's intention and serve as a catalyst for the further development of this fascinating and fertile mathematical field.' J. A. G. Vickers, Bulletin of the London Mathematical Society

• 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.

'... contains so much useful information ... I am sure that the book will fulfil its author's intention and serve as a catalyst for the further development of this fascinating and fertile mathematical field.' J. A. G. Vickers, Bulletin of the London Mathematical Society

• 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.

'... contains so much useful information ... I am sure that the book will fulfil its author's intention and serve as a catalyst for the further development of this fascinating and fertile mathematical field.' J. A. G. Vickers, Bulletin of the London Mathematical Society