We use high-precision photometry of red-giant-branch (RGB) stars in 57 Galactic globular clusters (GCs), mostly from the `Hubble Space Telescope (HST) UV Legacy Survey of Galactic GCs', to identify and characterize their multiple stellar populations. For each cluster the pseudo-two-colour diagram (or `chromosome map') is presented, built with a suitable combination of stellar magnitudes in the F275W, F336W, F438W, and F814W filters that maximizes the separation between multiple populations. In the chromosome map of most GCs (type-I clusters), stars separate in two distinct groups that we identify with the first (1G) and the second generation (2G). This identification is further supported by noticing that 1G stars have primordial (oxygen-rich, sodium-poor) chemical composition, whereas 2G stars are enhanced in sodium and depleted in oxygen. This 1G-2G separation is not possible for a few GCs where the two sequences have apparently merged into an extended, continuous sequence. In some GCs (type-II clusters) the 1G and/or the 2G sequences appear to be split, hence displaying more complex chromosome maps. These clusters exhibit multiple subgiant branches (SGBs) also in purely optical colour-magnitude diagrams, with the fainter SGB joining into a red RGB which is populated by stars with enhanced heavy-element abundance. We measure the RGB width by using appropriate colours and pseudo-colours. When the metallicity dependence is removed, the RGB width correlates with the cluster mass. The fraction of 1G stars ranges from ˜8 per cent to ˜67 per cent and anticorrelates with the cluster mass, indicating that incidence and complexity of the multiple population phenomenon both increase with cluster mass.