The correlations and fluctuations in Cu(DCOO)(2). 4D(2)O, which is a good physical realization of the 2D S = 1/2 Heisenberg antiferromagnet on a square lattice, have been measured by neutron scattering measurements. The quantum fluctuations cause a non-uniform. renormalization of the spin-wave dispersion with a zone boundary dispersion of 7%, while the spin wave amplitude is reduced to 51 +/- 4% of its classical value. The temperature dependence of the correlation length, the spin-wave damping and the spin-wave softening agrees with theoretical predictions over a large temperature range.