TITLE: Survey papers on the role played by PDE in mathematics
QUESTION [7 upvotes]: There are already several questions on MathOverflow that inquire about the many diverse relationships between PDE and several other 'areas' of mathematics (e.g., algebraic and differential geometry and topology, number theory, harmonic analysis, probability theory, dynamical systems, etc.); however, most of the answers give only a few particular examples. 
The aim of this question is to collect a [big-list] of references (i.e., broad surveys or monographs) that specifically focus on the role played by PDE in various other areas of mathematics, or on methods "stemming from other topics" that are used in the analysis of PDE.

REPLY [4 votes]: Klainerman, Partial Differential Equations, in Princeton Companion to Mathematics; a longer version is freely available here;
Klainerman, PDE as a Unified Subject;
Brezis and Browder, Partial Differential Equations in the 20th Century;
Yau, The Role of Partial Differential Equations in Differential Geoemtry;
Evans, Weak KAM Theory and Partial Differential Equations; 
Stroock, Partial Differential Equations for Probabilists;
etc.