Collisionless kinetic theory of the merging instability of magnetic islands is presented. Merging instability results in a very fast coalescence of attracting magnetic islands and may play an important role in magnetic energy release in solar flares and laboratory plasma devices. The general picture of merging instability regimes dependent on the value of magnetic shear and magnetic island width w is sketched. The new kinetic regime of collisionless coalescence with gamma approximately w1/2 which operates in a very wide parameter range is discussed in detail.