A study of sigma models whose target space is a group G that admits a
compatible Poisson structure is presented. The natural action of O(D,D;Z) on
the generalised tangent bundle TG+T*G and a generalisation of the Courant
bracket that appears are reviewed. This background provides a concrete example
where the generalised geometry and doubled geometry descriptions are both well
understood. Connections between the two formalisms are discussed and the
world-sheet theory from Hamiltonian and Lagrangian perspectives is
investigated. The comparisons between the approaches given by generalised
geometry and doubled geometry suggest possible ways of generalising the
analysis beyond the known examples.Comment: 43 page