We present a quantitative analysis of the star formation history (SFH) of 12 fields in the Small Magellanic Cloud (SMC) based on unprecedented deep [(B-R),R] color-magnitude diagrams (CMDs) from Nöel et al. (2007). Our fields reach down to the oldest main sequence (MS) turnoff with high photometric accuracy, which is vital for obtaining accurate SFHs. We use the IAC-pop code (Aparicio & Hidalgo 2009) to obtain the SFH, using a single CMD generated using IAC-star (Aparicio & Gallart 2004). We find that there are three main periods of enhancement of star formation: a young one peaked at ∼0.2-0.5 Gyr old, only present in the eastern and in the central-most fields; one at intermediate ages, peaked at ∼4-5 Gyr old in all fields; and an old one, peaked at ∼10 Gyr in all the fields but the western ones, in which this old enhancement splits into two, peaked at ∼8 Gyr old and at ∼12 Gyr old. This "two-enhancement" zone seems to be a robust feature since it is unaffected when using different stellar evolutionary libraries, implying that stars in the SMC take a Hubble time or more to mix. This indicates that there was a global enhancement in ψ(t) at ∼4-5 Gyr ago in the SMC. We also find that the age of the old population is similar at all radii and at all azimuth and we constrain the age of this oldest population to be older than ∼11.5 Gyr old. The intermediate-age population, in turn, presents variations with both, radii and azimuth. Theoretical studies based on results from larger spatial areas are needed to understand the origin of the young gradient. This young component is highly affected by interactions between Milky Way/LMC/SMC. We do not find yet a region dominated by an old, Milky Way-like, halo at 4.5 kpc from the SMC center, indicating either that this old stellar halo does not exist in the SMC or that its contribution to the stellar populations, at the galactocentric distances of our outermost field, is negligible. © 2009 International Astronomical Union.