  We investigate the capabilities of various stages of the SKA to perform
world-leading weak gravitational lensing surveys. We outline a way forward to
develop the tools needed for pursuing weak lensing in the radio band. We
identify the key analysis challenges and the key pathfinder experiments that
will allow us to address them in the run up to the SKA. We identify and
summarize the unique and potentially very powerful aspects of radio weak
lensing surveys, facilitated by the SKA, that can solve major challenges in the
field of weak lensing. These include the use of polarization and rotational
velocity information to control intrinsic alignments, and the new area of weak
lensing using intensity mapping experiments. We show how the SKA lensing
surveys will both complement and enhance corresponding efforts in the optical
wavebands through cross-correlation techniques and by way of extending the
reach of weak lensing to high redshift.
