A water distiller (10 or 100 or 200), with saturated hot humid air currents and recovery of latent heat of condensation, of the kind in which: - a number N of distillation units is provided, the unit in row 1 being the least hot and the unit in row N the hottest, - each of these N distillation units comprises a pair of vertical chambers, one for water evaporation and the other for vapour condensation, communicating from above; - each of these N evaporation chambers is occupied by a set of wettable or hydrophilic components (20 or 104 or 210); - each of these N condensation chambers is occupied by a hollow heat exchange device (22 or 120 or 212), these N devices being connected in series; - means (38 or 153 or 216) are connected to the apparatus to supply it with a stream of water, with a mass flow rate Q E0, at an initial low temperature T E0, to circulate this stream of water from bottom to top in the N hollow heat exchange devices; - a boiler (42 or 134 or 226) is connected to the outlet of the N hollow heat exchange devices to bring the water stream at temperature T E1 leaving them to a high temperature T E2 of less than 100°C; - means (52 or 142 or 228-236-244-252) are installed in the appliance to spread this hot water at temperature T E2 over the top of the components of the evaporation chamber of row N and to cause it to flow along the components of the evaporation chambers of rows (N-1) to 1; - means (34 and 170-172) or (116 and 148 1-4) or (260 1-4) are installed in the apparatus for forcing N adjusted flows of saturated moist hot air to circulate, from bottom to top in the N evaporation chambers and from top to bottom in the N condensation chambers, in order to respectively bring the N air currents, circulating at the top of the evaporation chambers, to predetermined temperatures T A1 to T AN, said means comprising means for blowing air at the bottom of the rank 1 evaporation chamber and means for adjusting the cross-sections of the communication paths between chambers of the distillation units; - means for collecting the distilled water flows (56 or 126 or 266) are installed at the bottom of the condensation chamber of row 1; - means for collecting the flow rates of concentrated aqueous solution (60 or 119 or 254) are installed at the bottom of the row 1 evaporation chamber; characterized in that: - the N heat exchange devices (221-6 or 120 1-4 or 212) have cross-sections and heights substantially identical to those of the N condensation chambers; - these N heat exchange devices are groups of hollow polymer plates (23, 121, 213), assembled separately at constant pitch, each group being provided with upstream and downstream collectors; - in the N condensation chambers, the hollow plates are installed vertically. - a number N of distillation units is provided, the unit in row 1 being the least hot and the unit in row N the hottest, - each of these N distillation units comprises a pair of vertical chambers, one for water evaporation and the other for vapour condensation, communicating from above; - each of these N evaporation chambers is occupied by a set of wettable or hydrophilic components (20 or 104 or 210); - each of these N condensation chambers is occupied by a hollow heat exchange device (22 or 120 or 212), these N devices being connected in series; - means (38 or 153 or 216) are connected to the apparatus to supply it with a stream of water, with a mass flow rate Q E0, at an initial low temperature T E0, to circulate this stream of water from bottom to top in the N hollow heat exchange devices; - a boiler (42 or 134 or 226) is connected to the outlet of the N hollow heat exchange devices to bring the water stream at temperature T E1 leaving them to a high temperature T E2 of less than 100°C; - means (52 or 142 or 228-236-244-252) are installed in the appliance to spread this hot water at temperature T E2 over the top of the components of the evaporation chamber of row N and to cause it to flow along the components of the evaporation chambers of rows (N-1) to 1; - means (34 and 170-172) or (116 and 148 1-4) or (260 1-4) are installed in the apparatus for forcing N adjusted flows of saturated moist hot air to circulate, from bottom to top in the N evaporation chambers and from top to bottom in the N condensation chambers, in order to respectively bring the N air currents, circulating at the top of the evaporation chambers, to predetermined temperatures T A1 to T AN, said means comprising means for blowing air at the bottom of the rank 1 evaporation chamber and means for adjusting the cross-sections of the communication paths between chambers of the distillation units; - means for collecting the distilled water flows (56 or 126 or 266) are installed at the bottom of the condensation chamber of row 1; - means for collecting the flow rates of concentrated aqueous solution (60 or 119 or 254) are installed at the bottom of the row 1 evaporation chamber; - the N heat exchange devices (221-6 or 120 1-4 or 212) have cross-sections and heights substantially identical to those of the N condensation chambers; - these N heat exchange devices are groups of hollow polymer plates (23, 121, 213), assembled separately at constant pitch, each group being provided with upstream and downstream collectors; - in the N condensation chambers, the hollow plates are installed vertically.