The fields of (i) nonlinear analysis, (ii) ODE and PDE, (iii) dynamical systems, and (iv) mathematical physics (e.g., electromagnetism, general relativity, gravitation, etc,...) are very huge, fertile, and, in a sense, unorganized (see, for example, Open problems in PDEs, dynamical systems, mathematical physics on MathOverflow).
Yet, they seem to me extremely interconnected; however, it seems also difficult to grasp a general (more or less) precise idea of their relationships (i.e.: the differences among their aims, and among the topics, problems, ideas, methods, etc. that they study).
Apparently, prof. S. Klainerman, in his survey paper PDE as a Unified Subject, gives a somewhat clear picture of "the area of PDE". This leads me to the following question:
Question:
Can you point out some (several) survey papers (somewhat in the spirit of Klainerman's) that offer a clear precise * (as much as possible) overview of the areas (i), (ii), (iii), (iv) with their problems and their key ideas, and possibly highlight their mutual relationships, the history of their developement and their relevance in mathematics (and also in science)?