This special issue commemorates the bicentenary of the birth of Évariste Galois who introduced the notion of a group and made fundamental contributions to the solution of polynomial equations. The formal mathematical concept of symmetry thus came from the Galois theory. Symmetry has been inaugurated and utilized in the solution of differential equations by Sophus Lie. The algebraic approach has thus become of great importance in the theory and applications of differential equations. There was recently Conference SDEA2012 on this topic held in Johannesburg during 23 to 27 January 2012 (http://www.wits.ac.za/conferences/sdea/12891/sdea2012.html).

SDEA2012 brought together researchers from all over the world to exchange ideas, share their research findings, and identify future research directions in symmetry and its manifold applications.

The special issue is not limited to the selected conference papers but also welcomes submissions from outside contributors. We invite conference participants and researchers to contribute original research articles and reviews to this special issue. Potential topics include, but are not limited to:

• Lie approaches to perturbed and complex differential equations
• Noether symmetries and their extensions
• Other methods for first integrals and conservation laws
• Linearization
• Classification schemes
• Invariant characterization
• Stochastic differential equations
• Geometrical methods
• Computational methods
• Symmetries of difference equations
• Symmetries in classical mechanics, continuum mechanics, and general relativity
• Application in finance and mathematical modeling
• Applications in theoretical physics, cosmology, and quantum gravity

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/jam/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/submit/journals/jam/sdea/ according to the following timetable: