The main focus in this area is a geometric approach to Hamiltonian systems and their manifestation in areas such as mechanics and fluid dynamics. Topics range from fundamental aspects of symplectic and multi-symplectic geometry to their applications to (quasi-)periodically forced systems, bifurcation theory, structure preserving discretizations and data assimilation, and to studies of specific systems such as N-body problems, electronic circuits, Josephson junctions, weather prediction and oceanographic waves. A particular emphasis is placed on studying the consequences of symmetries possessed by these systems. Cross-disciplinary research topics includes the dynamics of spacecraft (with the Surrey Space Centre) and environmental fluid flows (with the Fluid Dynamics Group and the Centre for Environmental Strategy).