Kepler Telescope was a space telescope launched in 2009, monitoring the brightness of 145,000 main sequence stars (or 190,000 according to another report). It operated until 2018 when its fuel ran out, operating in a reduced mode (K2) after an equipment failure in 2013.
It was a Schmidt camera with a 1.4 meter primary mirror and 95 megapixel CCD. It was designed specifically to locate extra-solar planets by monitoring for transients suggesting transiting planets. The original operation was continuous monitoring of a 116 square-degree field centered on right ascension 19h22'40", declination +44°30'00".
As of 2/2019, Kepler (including K2) is credited with 2700 candidates confirmed to be planets, plus 2800 additional candidates that await such confirmation, and past experience suggests 90% of such candidates are eventually confirmed to be planets, others being attributable to star spots or binary stars. With the sheer number of Kepler-candidates quickly produced, some other projects to find planet candidates were soon curtailed or abandoned.
Kepler also spotted stellar flares, interestingly, in Sun-like stars, with energies as much as 10,000 times what's been observed on the Sun, i.e., 1036 ergs.
A failure in May 2013 (a reaction wheel failure) compromised Kepler's precision, bringing its primary mission to a close, though with many planet-candidates yet to be checked, more discoveries will still be announced in the future. Alternate methods of spacecraft handling and planet hunting requiring less precision were devised, and a "second mission", named K2 followed.
The Kepler dichotomy is an observed trend in the data collected from Kepler: the count of systems showing one planet doesn't seem to fit in with the counts of those showing more planets. This has led to theories holding that some systems generate and evolve planets in a manner likely to result in a single planet and others use a mechanism likely to result in two or more.
Data on G-type stars and K-type stars has been studied as a single group (GK dwarfs), particularly to determine the distribution of planet counts for such stars.
KOI stands for Kepler object of interest, the term for a possible planet, i.e., the location of observations that appear to reveal a transiting planet.
KIC stands for Kepler Input Catalog, a catalog of the relevant stars in the Kepler field.