An introduction into the basic ideas of ab initio molecular dynamics methods is given. These methods unify molecular dynamics simulations and electronic structure calculations in the sense that the interactions, i.e. the forces used to propagate the classical nuclei, are obtained from concurrent or �on the fly� electronic structure calculations. Several such molecular dynamics schemes are discussed which arise from a sequence of approximations to the fully coupled Schr ̈odinger equation for electrons and nuclei. Special attention is devoted to Car�Parrinello methods being characterized by a fictitious dynamics of the electronic degrees of freedom.