Differential Geometry

• Differential Geometry of Curves & Surfaces - S. Kobayashi.

• Linear Algebra & Differential Geometry - M.M. Postnikoov.

• Differential Geometry & Lie Groups - M.M. Postnikov.

• Topics in Differential Geometry - Peter W. Michor

• Differential Geometry Vol I & II - S. Sobayashi

Undergraduate Analysis

• Analysis I & II - Terence Tao (Most favourite text on Analysis).

• Analysis I & II - Vladimir Zorich.

• Multidimensional Real Analysis - J. J. Duistermaat ( a pure beast and most preffered book for me).

• Differential Calculus on Normed Spaces - Henri Cartan (one of my favorite that I ever read)

• Foundation of Modern Analysis by J.Dieudonne".

• A Companion to Analysis: A Second First and First Second Course in Analysis -T. W. Körner.

• Elementary Real & Complex Analysis - Georgi Shilov.

• Mathematical Analysis : Linear & Metric Structure & Continuity - Mariano Giaquinta.

• Mathematical Analysis : Foundation & Advanced Techniques for function of Several Variables - Mariano Giaquinta.

Graduate Analysis

• Introductory Real Analysis - Kolmogorov & Fomin

• Integral, Measure and Derivative : A Unified Approach - Shilov

• Introduction to Measure Theory and Integration - Luigi Ambrosio

• Measure and Integration - Dietmar A. Salamon and has written really fantastic text on Functional Analysis. His mathematical life is very inspiring for me.

• Introduction to Measure Theory - Terence Tao

• A Comprehensive Course in Analysis - Barry Simon (I don't think there is any parallel of this mammoth work of Barry Simon)

• An Epsilon of Room I \& II - Terence Tao (perhaphs he is the only Fields Medalist, IMHO, with such a distinction of writing a UG \& Grad level lucid textbooks).

• Measure theory - Vladimir Bogachev (I would say that these two volumes are deepest and most comprehensive treatise on the Measure Theory).

Functional Analysis

• History of functional analysis - Jean Dieudonne. Can only be read after doing a course on FA. Dieudonne has also written on "History of Algebraic & Differential Topology".

• Elementary Functional Analysis - Georgi Shilov. Just assumes knowledge of metric spaces. Fine & lucid. A nice textboook for first reading.

• Elements of Theory of Functions and Functional Analysis - Kolmogorov & Fomin. First reading.

• Elements of Functional Analysis - L. A. Liusternik. First reading.

• An Introduction to Functional Analysis - James C. Robinson. Does now assumes any knolwedge of Measure Theory. First reading.

• Linear Functional Analysis - J. Cerda. One of its kind on the LFA. I came across this one when I was self learning the course in 2017. Can be read after doing any one of those textbook listed above.

• Functional Analysis - Theory and Applications - R.R. Edwards. There is no parallel of this book in terms of breadth, depth, lucidty and coherent ogrnisation of material. First or second Reading.

• Functional Analysis - Frigyes Riesz. One of the foremost fogure in FA. Its old style, very rigorous, hard, and original account of the Subject. Not for first Reading.

• Functional Analysis - Kosaku Yoshida. Only for second and preferably, the third reading of the subject.

• Functional Analysis -  Barry Simon. It is one from "Poincare Prize winning mathematician Barry Simon" - "Methods of Mathematical Physics Reed & Simon". Therefore, expect discussions on functional analytic aspect of Quantum Mechanics. "Simon & Reed" has been called as greatest tretaise on Mathematical Physics that was written in the last century.

• Functional Analysis - Dietmar Salamon. The second chapter is so nice on the three of the most important theorem of Functional Analysis. In fact one can find very good proofs and remark of Open Mapping, Hahn Banach Theorem, Uniform Boundedness Principle in the Marsden's mammoth text- "Manifolds, Tensor Analysis, and Applications" in Chapter 2 along with fanatsic theory of differential calculus in Banach Spaces (second chapter) of this impressive book - with fine collection of exercises.

• Problems in Real and Functional Analysis - Alberto Torchinsky.