  Short duration lensing events tend to be generated by low-mass lenses or by
lenses with high transverse velocities. Furthermore, for any given lens mass
and speed, events of short duration are preferentially caused by nearby lenses
(mesolenses) that can be studied in detail, or else by lenses so close to the
source star that finite-source-size effects may be detected, yielding
information about both the Einstein ring radius and the surface of the lensed
star. Planets causing short-duration events may be in orbits with any
orientation, and may have semimajor axes smaller than an AU, or they may reach
the outer limits of their planetary systems, in the region corresponding to the
Solar System's Oort Cloud. They can have masses larger than Jupiter's or
smaller than Pluto's. Lensing therefore has a unique potential to expand our
understanding of planetary systems. A particular advantage of lensing is that
it can provide precision measurements of system parameters, including the
masses of and projected separation between star and planet. We demonstrate how
the parameters can be extracted and show that a great deal can be learned. For
example, it is remarkable that the gravitational mass of nearby free-floating
planet-mass lenses can be measured by complementing observations of a
photometric event with deep images that detect the planet itself. A fraction of
short events may be caused by high-velocity stars located within a kpc. Many
high-velocity lenses are likely to be neutron stars that received large natal
kicks. Other high-speed stars may be members of the halo population. Still
others may be hypervelocity stars that have been ejected from the Galactic
Center, or runaway stars escaped from close binaries, possibly including the
progenitor binaries of Type Ia supernovae.
