Includes bibliographical references.

An overview of Lie's linesphere correspondence ; Application of Lie group analysis to a mathematical model which describes HIV transmission ; Geometry and PDE on the Heisenberg group: a case study ; Invariant evolutions of curves and surfaces and completely integrable Hamiltonian systems ; On the fixed points of the Toda hierarchy ; Group invariant solutions in mathematical physics and differential geometry ; Discrete symmetries of differential equations ; Integrable geometric evolution equations for curves ; On integrability of evolution equations and representation theory ; Symmetry groups, nonlinear partial differential equations, and generalized functions ; Lie symmetries of differentialdifference equations ; On a variational complex for difference equations ; The invariant variational bicomplex ; On geometrically integrable equations and hierarchies of pseudospherical type ; Inductive construction of moving frames ; Orbit reduction of contact ideals ; About the local and formal geometry of PDE ; Open problems in symmetry analysis R Milson ; V Torrisi and M C Nucci ; Richard Beals ; G Mari Beffa ; Barbara A Shipman ; I M Anderson M E Fels and C G Torre ; P E Hydon ; Thomas A Ivey ; Jan A Sanders and Jing Ping Wang ; Michael Oberguggenberger ; R Hernandez Heredero ; Elizabeth L Mansfield and Peter E Hydon ; Irina A Kogan and Peter J Olver ; Enrique G Reyes ; Irina A Kogan ; Vladimir Itskov ; Thierry Robart ; Peter A Clarkson and Elizabeth L Mansfield