  Gravitational microlensing occurs when a foreground star happens to pass very
close to our line of sight to a more distant background star. The foreground
star acts as a lens, splitting the light from the source star into two images,
which are typically unresolved. However, these images are also magnified, by an
amount that depends on the angular lens-source separation. The relative
lens-source motion results in a time-variable source magnification: a
microlensing event. If the foreground star happens to host a planet with
projected separation near the paths of these images, the planet will further
perturb the images, resulting in a characteristic, short-lived signature of the
planet. This chapter provides an introduction to the discovery and
characterization of exoplanets with gravitational microlensing. The theoretical
foundation of the method is reviewed, focusing on the phenomenology of
planetary perturbations. The strengths and weaknesses of the microlensing
technique are discussed, highlighting the fact that it is sensitive to low-mass
planets with separations just beyond the snow line, orbiting stars located
throughout the Galactic disk and foreground bulge. An overview of the practice
of microlensing planet searches is given, with a discussion of some of the
challenges with detecting and analyzing planetary perturbations. The chapter
concludes with a review of the results that have been obtained to date, and a
discussion of the near and long-term prospects for microlensing planet surveys.
Ultimately, microlensing is potentially sensitive to multiple-planet systems
containing analogs of all the solar system planets except Mercury, as well as
to free floating planets, and will provide a crucial test of planet formation
theories by determining the demographics of planets throughout the Galaxy.
