We report the detection of extended Ly alpha haloes around 145 individual star-forming galaxies at redshifts 3 <= z <= 6 in the Hubble Ultra Deep Field observed with the Multi-Unit Spectroscopic Explorer (MUSE) at ESO-VLT. Our sample consists of continuum-faint (-15 >= M-UV >= -22) Ly alpha emitters (LAEs). Using a 2D, two-component (continuum-like and halo) decomposition of Ly alpha emission assuming circular exponential distributions, we measure scale lengths and luminosities of Ly alpha haloes. We find that 80% of our objects having reliable Ly alpha halo measurements show Ly alpha emission that is significantly more extended than the UV continuum detected by HST (by a factor approximate to 4 to >20). The median exponential scale length of the Ly alpha haloes in our sample is approximate to 4.5 kpc with a few haloes exceeding 10 kpc. By comparing the maximal detected extent of the Ly alpha emission with the predicted dark matter halo virial radii of simulated galaxies, we show that the detected Ly alpha emission of our selected sample of Ly alpha emitters probes a significant portion of the cold circum-galactic medium of these galaxies (>50% in average). This result therefore shows that there must be significant HI reservoirs in the circum-galactic medium and reinforces the idea that Ly alpha haloes are ubiquitous around high-redshift Ly alpha emitting galaxies. Our characterization of the Ly alpha haloes indicates that the majority of the Ly alpha flux comes from the halo (approximate to 65%) and that their scale lengths seem to be linked to the UV properties of the galaxies (sizes and magnitudes). We do not observe a significant Ly alpha halo size evolution with redshift, although our sample for z > 5 is very small. We also explore the diversity of the Ly alpha line profiles in our sample and we find that the Ly alpha lines cover a large range of full width at half maximum (FWHM) from 118 to 512 km s(-1). While the FWHM does not seem to be correlated to the Ly alpha scale length, most compact Ly alpha haloes and those that are not detected with high significance tend to have narrower Ly alpha profiles (<350 km s(-1)). Finally, we investigate the origin of the extended Ly alpha emission but we conclude that our data do not allow us to disentangle the possible processes, i.e. scattering from star-forming regions, fluorescence, cooling radiation from cold gas accretion, and emission from satellite galaxies.