Hierarchical clustering scenarios for galaxy formation predict that dwarf galaxies are the first to be formed and that they are building blocks of larger galaxies. We propose here to measure the spatial structure and the stellar age and metallicity distribution of the Phoenix dwarf galaxy to give support or reject such scenarios. The kind of detailed study we propose can only be carried on in nearby dwarfs and using the HST. We intend to obtain very deep V and I color-magnitude diagrams reaching the oldest MS turn-offs of a central and an outer field of Phoenix. Applying our techniques based on synthetic color-magnitude diagrams, we will determine the stellar population {age and metallicity distribution} gradients as a function of the galactocentric distance. Combined with our previous ground-based study of the galaxy, this will provide evidences of whether or not Phoenix has a real ``disk/halo'' structure and will allow to trace out the early phases of its evolution.