I don't know whether I should ask this question here or not but I asked this question on MSE but didn't get any answer so I am posting it here.

Though similar questions have been asked at https://math.stackexchange.com/questions/2827/good-1st-pde-book-for-self-study and https://math.stackexchange.com/questions/194152/good-reference-texts-for-introduction-to-partial-differential-equation?lq=1 but none of them really answer my query, so I am bounded to ask this.

I am basically interested in Differential and Riemannian Geometry and one of my Professors told me that it will be a good idea if I acquire a sound knowledge of PDE. I know about the basics of PDE (i.e., methods of solving PDE ) but I don't have any firm knowledge of the analysis which goes on in there.

So, my question is that what will be a good textbook to start learning PDE that could help in undrstanding the $\it{analysis}$ portion as well as with applications of PDE in Differential/Riemannian Geometry.

Background : I have studied Measure Theory, Functional Analysis, Complex Analysis and some Fourier Analysis (from Stein & Shakarchi's book on Fourier Analysis). I am currently studying Algebraic Topology, Differential and Riemannian Geometry (from Do Carmo's book).

Thanks!!