Lie transformation groups and Lie group generators.
Prolongations and Lie algebras.
Lie point symmetries: Invariance of the differential equations.
Applications to ODEs.
Applications to PDEs.
Lie-Baecklund symmetries, recursion operators and integrability.
Transformations between differential equations.
Symmetry Methods for Differential Equations: A Beginner's Guide
P. E. Hydon (Cambridge University Press - 2000)
Symmetries of Differential Equations
G. W. Bluman and S. Kumei (Springer-Verlag - 1989)
Symmetries and Integration Methods for Differential
Equations
G. W. Bluman and S. C. Anco (Springer-Verlag - 2002)
Applications of Lie Groups to Differential Equations
P. J. Olver (Springer-Verlag - 1st edition 1986 and 2nd edition 1993)