  We present a new numerical code designed to solve the Einstein field
equations for axisymmetric spacetimes. The long term goal of this project is to
construct a code that will be capable of studying many problems of interest in
axisymmetry, including gravitational collapse, critical phenomena,
investigations of cosmic censorship, and head-on black hole collisions. Our
objective here is to detail the (2+1)+1 formalism we use to arrive at the
corresponding system of equations and the numerical methods we use to solve
them. We are able to obtain stable evolution, despite the singular nature of
the coordinate system on the axis, by enforcing appropriate regularity
conditions on all variables and by adding numerical dissipation to hyperbolic
equations.
