Abstract
The present article is concerned with research in the last five to ten years on systems of linear partial differential equations. The total number of published works in this area, of course, is too great to cover each one in sufficient detail. While consciously refraining from undertaking such a task, I have endeavored to focus a proportionate amount of attention on each facet of the topic insofar as it embodies the characteristics which distinguish the theory of systems from the analogous theory of one equation in one unknown function. For example, considerable space is accorded the -Neumann problem, which is endowed with a specialized character and whose solution has contributed a great deal that is conceptually new to the general theory. On the other hand, the highly-developed theory of boundary-value problems is scarcely touched at all, as its methods pertain by and large to scalar theory.
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