For Functional Analysis, I'd recommend Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis. Some alternatives often suggested are the books by Kreyszig or Lax. Where they fall short depends on what your purpose of study is. To me, most students are learning functional analysis as a tool, usually for PDEs at the level of Evans or John and Brezis is the most versatile book for this or other purposes. It's exposition is lucid and the exercises come with partial solutions. Kreyszig has a lot of overlap but it's more restrictive in its proofs and presentation. Lax's presentation of the topics is non-standard a number of times and should be used as a complementary text to Brezis. All this being said, for PDE I would always recommend learning Harmonic Analysis and the Theory of Distributions in conjunction with what is considered the classical functional analysis course centered around the results of Banach. Harmonic Analysis is hard to find a good singular reference for (at this level, serving this purpose) but there are bits and pieces of notes online that I patched together to gather some understanding and the Theory of Distributions could probably be learned from a combination of Folland's chapter 9, Stein-Shakarchi Book 4, and the book by Friedlander.
For Functional Analysis, I'd recommend Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis. Some alternatives often suggested are the books by Kreyszig or Lax. Where they fall short depends on what your purpose of study is. To me, most students are learning functional analysis as a tool, usually for PDEs at the level of Evans or John and Brezis is the most versatile book for this or other purposes. It's exposition is lucid and the exercises come with partial solutions. Kreyszig has a lot of overlap but it's more restrictive in its proofs and presentation. Lax's presentation of the topics is non-standard a number of times and should be used as a complementary text to Brezis. All this being said, for PDE I would always recommend learning Harmonic Analysis and the Theory of Distributions in conjunction with what is considered the classical functional analysis course centered around the results of Banach. Harmonic Analysis is hard to find a good singular reference for (at this level, serving this purpose) but there are bits and pieces of notes online that I patched together to gather some understanding and the Theory of Distributions could probably be learned from a combination of Folland's chapter 9, Stein-Shakarchi Book 4, and the book by Friedlander.