We have undertaken a comprehensive search for both Lyman alpha emitters (LAEs) and Lyman break galaxies (LBGs) in the Survey for High-z Absorption Red and Dead Sources (SHARDS) Survey of the Great Observatories Origins Deep Survey North field. SHARDS is a deep imaging survey, made with the 10.4 m Gran Telescopio Canarias, employing 25 medium band filters in the range from 500 to 941 nm. This is the first time that both LAEs and LBGs are surveyed simultaneously in a systematic way in a large field. We draw a sample of 1558 sources; 528 of them are LAEs. Most of the sources (1434) show rest-frame UV continua. A minority of them (124) are pure LAEs with virtually no continuum detected in SHARDS. We study these sources from z ˜ 3.35 up to z˜ 6.8, well into the epoch of reionization. Note that surveys done with just one or two narrow band filters lack the possibility to spot the rest-frame UV continuum present in most of our LAEs. We derive redshifts, star formation rates, Lyα equivalent widths, and luminosity functions (LFs). Grouping within our sample is also studied, finding 92 pairs or small groups of galaxies at the same redshift separated by less than 60 comoving kpc. In addition, we relate 87 and 55 UV-selected objects with two known overdensities at z = 4.05 and z = 5.198, respectively. Finally, we show that surveys made with broad-band filters are prone to introduce many unwanted sources (˜20 per cent interlopers), which means that previous studies may be overestimating the calculated LFs, specially at the faint end.