In this thesis I focused on the study of the dwarf galaxies in the Local Group (LG). Since they can be resolved into stars, this group of galaxies offers a perfect laboratory to address the still open problems in galaxy formation and evolution. In addition, the LG is composed by a unique mixture of all the morphological types of dwarfs, namely dwarf irregulars (dIrr), spheroidals (dSph), and the recently discovered ultra faints (UFD). The star formation histories (SFH) of these systems are fundamental to obtain deeper insights into their stellar populations, and especially on the presence of radial gradients.
The sample of galaxies analysed in the present study is composed by a dIrr, two dSphs, and a UFD. These are NGC 6822, Draco, Ursa Minor (UMi), and Hercules, respectively.
In all the cases the photometry was obtained using DAOPHOT/~ALLSTAR/~ALLFRAME (Stetson 1987, 1994), which resulted in the derivation of very accurate colour-magnitude diagrams (CMD). The study of NGC 6822 is based on HST data, whereas in all the other cases Subaru data have been used. In addition, in the case of NGC 6822 and Draco the accurate star formation history was derived using the IAC method composed of IACs-tar/IAC-pop/MinnIAC (Aparicio & Gallart 2004; Aparicio & Hidalgo 2009; Hidalgo et al. 2011).
The data sample of NGC 6822 is divided into six fields, which cover the whole bar of this dwarf galaxy. The SFH solutions we derived show an enhanced star formation rate (SFR) in Fields 1 and 3 during the past 500 Myr, whereas the SFRs in the other fields are almost extinguished at very recent epochs. In addition, I studied the radial gradients of the populations by considering the total mass converted into stars in two time intervals (between 0 and 0.5 Gyr ago and between 0.5 and 13.5 Gyr ago). The scale lengths of the young and intermediate-to-old populations result perfectly compatible, with the exception of the young populations in Fields 1 and 3. The recent SFR in these two fields is greater than in the other ones. This might be an indication that in these two fields we are sampling incipient spiral arms. In addition, the age-metallicity relations were derived. As expected, the metallicity increases with time for all of the fields. No radial gradient in the metallicity is observed.
The data available for the dSph Draco are composed of five fields, which cover as far out as 3 core radii. The SFH of Draco is characterized by a unique burst which took place approx. 12.9 Gyr ago, with a width of approx. 0.5 Gyr. This is compatible with a quenching of the SF activity due to the effect of reionization, even though a signature in the spectroscopic measurement of the metallicity rises doubts about this interpretation. In addition, I studied the presence of radial gradients in Draco. I calculated the scale lengths of different evolutionary features of this galaxy. All the scale lengths are compatible, hence there is evidence that Draco is composed by a unique stellar population.
For UMi the SFH was not obtained, because of a significant difference between the predictions of the evolutionary models and the observed CMD. A real peculiarity in this galaxy is excluded if archival HST photometry is considered, which agrees with the models. Hence I requested two additional sets of data, obtained with the IAC80 and NOT telescope. The first dataset was used in order to verify the calibration equations obtained. The second one was used to investigate if a non lineariry between the data was present. None of the two data sets were useful to solve the discrepancy, hence I performed a study of the populations in this galaxy based on star counts. In particular, I compared the width of the observed sub-giant branch with that predicted by stellar evolutionary models. This comparison sheds light on the duration of the SF burst in UMi, which results to be between 0.15 and 2 Gyr. Moreover, I investigate the radial gradients in this dSph. As in the previous cases I derived the scale lengths for different evolutionary features in this galaxy, which are compatible within 3\sigma. Hence, UMi appears to be dominated by only one stellar population.
The photometry of Hercules turned out to be too shallow to derive the accurate SFH. Hence I compared it to a set of GGC and isochrones belonging to the BaSTI library (Pietrinferni et al. 2004). This comparison discloses that this galaxy hosts a population of age >12 Gyr and of very low metal content.