Lecture notes on geometrical aspects of partial differential equations Book

	Introduction
0	Infinite-Dimensional Differential Geometry
0.1	Manifolds	1
0.2	Vector Fields and Differential Forms	3
0.3	Mappings	9
0.4	Submanifolds	13
0.5	Involutive Distributions	23
0.6	Discussion	25
Ch. I	Internal Geometry of PDE
1	Differential Manifolds	36
2	Lie-Backlund Mappings	53
3	Lie-Backlund Fields and Infinitesimal Symmetries	85
4	Cartan forms, Currents and Conservation Laws	106
5	C-spectral Sequence. Further Properties of Conservation Laws	124
6	Trivial Equations. The Formal Variational Calculus	137
7	Evolution Equations	156
Ch. II	External Geometry of PDE
8	Differential Submanifolds	173
9	Normal Projection. External Fields and Forms	185
10	Trivial Ambient Differential Manifolds	202
11	The Characteristic Mapping	221
12	The Green's Formula	231
13	Low-dimensional Conservation Laws	239
14	Backlund correspondence	266
Ch. III	Further Studies
15	Lagrangian Formalism	283
16	Hamiltonian Equations	296
17	Example: The Nambu's String	317
	Appendix: Differential Algebras	337
	Bibliography	351
	Subject Index	357