We present the quantitative rest-frame B morphological evolution and galaxy merger fractions at 0.2 < z < 1.2 as observed by the All-wavelength Extended Groth Strip International Survey (AEGIS). We use the Gini coefficent and M_20 to identify major mergers and classify galaxy morphology for a volume-limited sample of 3009 galaxies brighter than 0.4 L_B^*, assuming pure luminosity evolution of 1.3 M_B per unit redshift. We find that the merger fraction remains roughly constant at 10 +/- 2% for 0.2 < z < 1.2. The fraction of E/S0/Sa increases from 21+/- 3% at z ~ 1.1 to 44 +/- 9% at z ~ 0.3, while the fraction of Sb-Ir decreases from 64 +/- 6% at z ~ 1.1 to 47 +/- 9% at z ~ 0.3. The majority of z < 1.2 Spitzer MIPS 24 micron sources with L(IR) > 10^11 L_sun are disk galaxies, and only ~ 15% are classified as major merger candidates. Edge-on and dusty disk galaxies (Sb-Ir) are almost a third of the red sequence at z ~ 1.1, while E/S0/Sa makeup over 90% of the red sequence at z ~ 0.3. Approximately 2% of our full sample are red mergers. We conclude (1) the galaxy merger rate does not evolve strongly between 0.2 < z < 1.2; (2) the decrease in the volume-averaged star-formation rate density since z ~ 1 is a result of declining star-formation in disk galaxies rather than a disappearing population of major mergers; (3) the build-up of the red sequence at z < 1 can be explained by a doubling in the number of spheroidal galaxies since z ~ 1.2.
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