Since Peter Lax was chosen as the recipient of the 2005 Abel Prize, it's hardly necessary to say that his work is important. Libraries should consider his Selected Papers an essential acquisition. The first volume collects papers on partial differential equations, difference equations approximating PDEs, hyperbolic systems of conservation laws, and integrable systems. This second volume includes many papers on scattering theory, a few on functional analysis, and several others that don't fit into tighter categories and are just included under "analysis" and "algebra".
List of Publications
Scattering Theory in Euclidean Space
Scattering Theory for Automorphic Functions