Abstract: A blood oxygenator for one time use and discard in medical procedures. The blood oxygenator has a unitary transparent sealed vessel with first and second blood treating stages arranged for series flow. The first stage receives an inflow of blood and oxygen and it has integrated oxygenating and heat exchanging elements that include a plurality of vertical ribs and flutes internested to provide upright thin-film blood and oxygen flow channels. These ribs and flutes surround, by a common wall, a heat exchanger with upright channels for counter-directional coolant flow relative to the blood and oxygen flow. The second stage has integrated blood degassing and defoaming elements including a vertical perforated wall surrounded by a porous foam member with a surrounding reservoir of outflowing degassed and defoamed blood and a vent for free oxygen gas.