  We study stationary and axisymmetric solutions of General Relativity, i.e.
pure gravity, in four or higher dimensions. D-dimensional stationary and
axisymmetric solutions are defined as having D-2 commuting Killing vector
fields. We derive a canonical form of the metric for such solutions that
effectively reduces the Einstein equations to a differential equation on an
axisymmetric D-2 by D-2 matrix field living in three-dimensional flat space
(apart from a subclass of solutions that instead reduce to a set of equations
on a D-2 by D-2 matrix field living in two-dimensional flat space). This
generalizes the Papapetrou form of the metric for stationary and axisymmetric
solutions in four dimensions, and furthermore generalizes the work on Weyl
solutions in four and higher dimensions. We analyze then the sources for the
solutions, which are in the form of thin rods along a line in the
three-dimensional flat space that the matrix field can be seen to live in. As
examples of stationary and axisymmetric solutions, we study the
five-dimensional rotating black hole and the rotating black ring, write the
metrics in the canonical form and analyze the structure of the rods for each
solution.
