In an ab initio molecular dynamics calculation, the finite-temperature dynamics of a system is generated using forces obtained directly from electronic structure calculations performed ``on the fly'' as the simulation proceeds. Within this approach, manybody forces, electronic polarization, and chemical bond-breaking and forming evnets are treated explicitly, thereby allowing chemical processes in condensed phases to be studied efficiently and with reasonable accuracy. The method of Car and Parrinello, first introduced in 1985, allows such calculations to be performed within the elegant framework of an extended Lagrangian and has become an immensely popular approach for performing ab initio molecular dynamics simulations. The aim of this tutorial is to develop the basic theory of ab initio molecular dynamics and its implementation via the Car-Parrinello method. Questions of how ab initio molecular dynamics is derived from the Schroedinger equation, adiabatic dynamics and the justification of the Car-Parrinello approach, and several algorithmic issues including basis sets and pseudopotentials will be addressed.