  We investigate the evolution of extinction curves in galaxies based on our
evolution model of grain size distribution. In this model, we considered
various processes: dust formation by SNe II and AGB stars, dust destruction by
SN shocks in the ISM, metal accretion onto the surface of grains (referred to
as grain growth), shattering and coagulation. We find that the extinction curve
is flat in the earliest stage of galaxy evolution. As the galaxy is enriched
with dust, shattering becomes effective to produce a large abundance of small
grains ($a \la 0.01\;\mu$m). Then, grain growth becomes effective at small
grain radii, forming a bump at $a \sim 10^{-3}${--}$10^{-2}\;\mu$m on the grain
size distribution. Consequently, the extinction curve at ultraviolet (UV)
wavelengths becomes steep, and a bump at $1/\lambda \sim 4.5\;\mu{\rm
m}^{-1}\;(\lambda: \mbox{wavelength})$ on the extinction curve becomes
prominent. Once coagulation becomes effective, the extinction curves become
flatter, but the UV extinction remains overproduced when compared with the
Milky Way extinction curve. This discrepancy can be resolved by introducing a
stronger contribution of coagulation. Consequently, an interplay between
shattering and coagulation could be important to reproduce the Milky Way
extinction curve.
