  Whereas considerable effort has been afforded in understanding the properties
of galaxies, a full physical picture, connecting their baryonic and dark-matter
content, super-massive black holes, and (metric) theories of gravity, is still
ill-defined. Strong gravitational lensing furnishes a powerful method to probe
gravity in the central regions of galaxies. It can (1) provide a unique
detection-channel of dark-matter substructure beyond the local galaxy group,
(2) constrain dark-matter physics, complementary to direct-detection
experiments, as well as metric theories of gravity, (3) probe central
super-massive black holes, and (4) provide crucial insight into galaxy
formation processes from the dark matter point of view, independently of the
nature and state of dark matter. To seriously address the above questions, a
considerable increase in the number of strong gravitational-lens systems is
required. In the timeframe 2010-2020, a staged approach with radio (e.g. EVLA,
e-MERLIN, LOFAR, SKA phase-I) and optical (e.g. LSST and JDEM) instruments can
provide 10^(2-4) new lenses, and up to 10^(4-6) new lens systems from
SKA/LSST/JDEM all-sky surveys around ~2020. Follow-up imaging of (radio) lenses
is necessary with moderate ground/space-based optical-IR telescopes and with
30-50m telescopes for spectroscopy (e.g. TMT, GMT, ELT). To answer these
fundamental questions through strong gravitational lensing, a strong investment
in large radio and optical-IR facilities is therefore critical in the coming
decade. In particular, only large-scale radio lens surveys (e.g. with SKA)
provide the large numbers of high-resolution and high-fidelity images of lenses
needed for SMBH and flux-ratio anomaly studies.
