  Almost toric manifolds form a class of singular Lagrangian fibered symplectic
manifolds that is a natural generalization of toric manifolds. Notable examples
include the K3 surface, the phase space of the spherical pendulum and rational
balls useful for symplectic surgeries. The main result of the paper is a
complete classification up to diffeomorphism of closed almost toric
four-manifolds.
  A key step in the proof is a geometric classification of the singular affine
structures that can occur on the base of a closed almost toric four-manifold.
