In the mid-18th century,Euler derived his famous equations of motion of an incompressible fluid, one ofthe most studied equations in hydrodynamics. More than 200 years later, in1966, Arnold observed that they are, in fact, geodesic equations on the(infinite dimensional) Lie group of volume-preserving diffeomorphisms of amanifold, endowed with a certain right-invariant Riemannian metric.