Hydrodynamic transport coefficients may be evaluated from first principles in a weakly coupled scalar field theory at arbitrary temperature. In a theory with cubic and quartic interactions, the infinite class of diagrams which contribute to the leading weak coupling behavior are identified and summed. The resulting expression may be reduced to a single linear integral equation, which is shown to be identical to the corresponding result obtained from a linearized Boltzmann equation describing effective thermal excitations with temperature dependent masses and scattering amplitudes. The effective Boltzmann equation is valid even at very high temperature where the thermal lifetime and mean free path are short compared to the Compton wavelength of the fundamental particles. Numerical results for the shear and the bulk viscosities are presented.

116 pages. An error in printing the figures file is corrected. The bulk viscosity sections are corrected and entirely rewritten. 38 figures in post-script format. One style file is included