We introduce the Assembling Galaxies Of Resolved Anatomy (AGORA) project, a comprehensive numerical study of well-resolved galaxies within the CDM cosmology. Cosmological hydrodynamic simulations with force resolutions of similar to 100 proper pc or better will be run with a variety of code platforms to follow the hierarchical growth, star formation history, morphological transformation, and the cycle of baryons in and out of eight galaxies with halo masses Mvir = 10 super(10), 10 super(11), 10 super(12), and 10 super(13) M= at z = 0 and two different assembly histories. The numerical techniques and implementations used in this project include the smoothed particle hydrodynamics codes Gadget and Gasoline, and the adaptive mesh refinement codes Art, Enzo, and Ramses. The initial conditions for the AGORA galaxies as well as simulation outputs at various epochs will be made publicly available to the community.