  Weak gravitational lensing of background galaxies provides a direct probe of
the projected matter distribution in and around galaxy clusters. Here we
present a self-contained pedagogical review of cluster--galaxy weak lensing,
covering a range of topics relevant to its cosmological and astrophysical
applications. We begin by reviewing the theoretical foundations of
gravitational lensing from first principles, with special attention to the
basics and advanced techniques of weak gravitational lensing. We summarize and
discuss key findings from recent cluster--galaxy weak-lensing studies on both
observational and theoretical grounds, with a focus on cluster mass profiles,
the concentration--mass relation, the splashback radius, and implications from
extensive mass calibration efforts for cluster cosmology.
