Integration of differential equations is a central problem in mathematics and several approaches have been developed by studying analytic, algebraic, and algorithmic aspects of the subject. One of these is Differential Galois Theory, developed by Kolchin and his school, and another originates from the Soliton Theory and Inverse Spectral Transform method, which was born in the works of Kruskal, Zabusky, Gardner, Green and Miura. Many other approaches have also been developed, but there has so far been no intersection between them. This unique introduction to the subject finally brings them together, with the aim of initiating interaction and collaboration between these various mathematical communities. The collection includes a LMS Invited Lecture Course by Michael F. Singer, together with some shorter lecture courses and review articles, all based upon a mini-programme held at the International Centre for Mathematical Sciences (ICMS) in Edinburgh.

'… a useful book that serves as an introduction to both the Galois theory of (linear) differential equations and several other algebraic approaches to such equations. Libraries will definitely want to have a copy.'

Source: MAA Reviews

'… useful for graduate mathematicians working in differential systems and their invariants. The text covers a large area of research on relatively few pages and contains many examples.'

Source: EMS Newsletter