The geometry of Lie algebroids and its applications to optimal control

The paper presents the geometry of Lie algebroids and its applications to optimal control. The first part deals with the theory of Lie algebroids, connections on Lie algebroids and dynamical systems defined on Lie algebroids (mainly Lagrangian and Hamiltonian systems). In the second part we use the framework of Lie algebroids in the study of distributional systems (drift less control affine systems) with holonomic or nonholonomic distributions.