This thesis focuses on the study of LAEs and LBGs at z=3.4-6.8, a period of time between ~0.8-2 Gyr after the Big Bang, hosting the end of the reionisation epoch. To reach such deep galaxies, we have made use of the SHARDS survey of the GOODS-N field, with 200 h of exposure time with GTC. The 25 consecutive medium-band filters in the optical/NIR have provided us with very good SEDs of these galaxies, which we have further completed with ancillary data from other previous deep observations of the field, allowing a comprehensive analysis of the SEDs.

In the first part of this work, we develop our own robust selection criteria, paying special attention to the interlopers rejection. The final selected sample consists of 1558 sources, divided in 528 LAEs and 1030 non-LAEs/LBGs. The comparison of this sample with previous broad-band studies has revealed that the latter are prone to introduce a non-negligible amount of low redshift interlopers due to the lack of good spectral resolution in their SEDs. From the SEDs in our sample, we have derived photometric redshifts, Ly alpha EWs, SFRs and LFs.

In order to calculate ages and stellar masses of our galaxies, we have carried out a SP synthesis modeling of the SEDs, using burst-like SFHs. We focus the SP analysis on differences between subfamilies of LAEs and LBGs, as well as on the need of one or two SPs to properly describe each SED. The results derived from the model fitting, joined to the relative fraction of each subfamily found at each z in this work, support an evolutionary relation from low mass LAEs to more massive LBGs. With the model-derived masses, we have built SMFs and estimated the SMD at different redshifts.

We have also performed a search for galaxies in close groups, reporting 92 of them, some with up to six members. Many of these groups show tail-like structures that point to a gravitational bound between their galaxies. Additionally, we have studied a previously discovered z=5.198 overdensity in GOODS-N, finding 44 new candidates within our sample. Some of them have been further confirmed through MOS observations. If most of the remaining new candidates are confirmed, this proto-cluster would be the most populated one up to date beyond z=5 in such a tight redshift range.

The final part of this thesis is dedicated to an unsupervised ML SEDs clustering of both our sample and the SC4K-COSMOS high-z LAEs sample. The results point to the Ly alpha line and the UV slope as the most relevant parameters driving the classes differentiation, separating sources with strong Ly alpha emission and blue UV slope from those with steeper slope and fainter line emission. The study of the median ages and stellar masses of the groups supports the evolutionary hypothesis between LAEs and LBGs subgroups. Moreover, the ML classification has shown to be very effective for the detection of some few remaining interlopers in both samples.