  In this article, we give the structure of codimension one foliations with
canonical singularities and numerically trivial canonical class on varieties
with klt singularities. Building on recent works of Spicer, Cascini - Spicer
and Spicer - Svaldi, we then describe the birational geometry of rank two
foliations with canonical singularities and canonical class of numerical
dimension zero on complex projective threefolds.
