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Prior to the publication of this book, the higher symmetries and conservation laws, together with similar strong results, were only known for partial differential equations with two independent variables. The first part of this work deals with the problem of how to find all higher symmetries and conservation laws for a given differential equation, illustrated by the equations of mathematical physics, most of them having more than two independent variables. The method presented for the generation of functions for finding conservation laws does not depend on any symmetry considerations. In particular, it works in situations where Noether-type theorems are not applicable.
In the second part, one can find some constructions of systems that are ‘integrable’ (in a sense), leading to the derivation of interesting relations between the two concepts of ‘integrability’ and ‘ symmetry’. The section closes with a discussion of some methods for modeling continuum media based on symmetry considerations.

It is now obvious that effective applications of symmetry methods to the investigation of concrete equations are impossible without considerable computer support. For this reason, the third part of the work is devoted to this topic.

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