  We extend Routh's reduction procedure to an arbitrary Lagrangian system (that
is, one whose Lagrangian is not necessarily the difference of kinetic and
potential energies) with a symmetry group which is not necessarily Abelian. To
do so we analyse the restriction of the Euler-Lagrange field to a level set of
momentum in velocity phase space. We present a new method of analysis based on
the use of quasi-velocities. We discuss the reconstruction of solutions of the
full Euler-Lagrange equations from those of the reduced equations.
