Calculus  

Summary [html].

1. A. I. Khinchin, ``A course of mathematical analysis,'' Translated from the 3d Russian ed., 1957. 
2. Boris Demidovich, ``Problems in Mathematical Analysis,'' Beekman Pub, 1975.
3. W. Fulks, ``Advanced calculus,''
4. Elliott Mendelson, Frank Ayres Jr., ``Schaum's Outline of Calculus,'' 4th ed., McGraw-Hill, 1999.
5. Murray R. Spiegel, ``Schaum's Outline of Advanced Calculus,'' McGraw-Hill, 1968.
6. Boris Demidovich (Editor), ``Problems in Mathl Analysis,'' Publishers Staff Mir (Translator), December 1975, ISBN: 0846407612.
7. I. S. Gradshteyn, I. M. Ryzhik, Alan Jeffrey (Editor), Daniel Zwillinger, ``Table of Integrals, Series, and Products,'' Academic Press; ISBN: 0122947576; 6th edition (July 31, 2000).

Measure Theory

Summary [html].

1. S. B. Chae, ``Lebesgue integration,'' 2nd Edition, Springer-Verlag, 1995.

Real Analysis

Summary [html].

1. David Bressoud, ``A Radical Approach to Real Analysis,'' Mathematical Association of America, 1994. (a great book for undergraduate)
2. Walter Rudin, ``Principles of mathematical analysis,'' 3d ed., New York : McGraw-Hill, 1976.
3. Walter Rudin, ''Real and complex analysis,'' 2d ed., New York, McGraw-Hill, 1974.

Complex Analysis

1. J. W. Brown and R. V. Churchill, ``Complex variables and applications,'' 6th Edition, McGraw-Hll, 1996.
2. P. Henrici, ``Applied and computational complex analysis,'' vol. 1 & 2, Wiley, 1974. ISBN: 0471372447 (v. 1)

Functional Analysis (Infinite-dimensional Spaces and Operator Theory)

Summary [html].

1. W. Rudin, ``Functional Analysis,'' 2nd ed., McGraw-Hll, 1991.
2. Erwin Kreyszig, ``Introductory functional analysis with applications,'' New York : Wiley, c1978. 
3. J. Tinsley Oden, ``Applied functional analysis : a first course for students of mechanics and engineering science,'' Englewood Cliffs, N.J. : Prentice-Hall, c1979. 
4. Ruth F. Curtain, A. J. Pritchard, ``Functional analysis in modern applied mathematics,'' London ; New York : Academic Press, 1977. 
5. Riesz and Nagy, 'Functional Analysis'.
6. Gelfand, et al., 'Generalized Functions' volumes 1-5
7. Dunford and Schwartz, 'Linear Operators, I,II,III'.
8. G.J. Murphy, 'C*-algebras and Operator Theory'.
9. Stein and Weiss, 'Introduction to Fourier Analysis on Euclidean Spaces'.
10. E.M. Stein, 'Harmonic Analysis'.
11. Conway J. "A course in functional analysis" 
12. Kirillov A.A. and Gvishiani A.D. "Theorems and problems in functional analysis" 
13. Kolmogorov A.A. and Fomin C.B.. "Elements of the theory of functions and functional analysis" vol.1,2 
14. Lusternik L.A. and Sobolev S.L. "Elements of functional analysis" 
15. Mukherjea A. and Pothovey "Real and functional analysis" 
16. Reed M. and Simon B. "Methods of modern mathematical physics. 1. Functional analysis" 
17. Taylor A.E. and Lay D.C. "Introduction to functional analysis" 
18. Yosida K. "Functional analysis"

19. Brychkov, Yu. A. and Prudnikov, A. P. Integral Transforms of Generalized Functions. New York: Gordon and Breach, 1989.

20. Kanwal, R. P. Generalized Functions: Theory and Technique, 2nd ed. Boston, MA: Birkhäuser, 1998.

21. M. J. Lighthill, Introduction to Fourier analysis and generalised functions. New York, Cambridge University Press, 1958.

    　

Vector Analysis

• Michael J. Crowe (1994). A History of Vector Analysis : The Evolution of the Idea of a Vectorial System. Dover Publications; Reprint edition. ISBN 0-486-67910-1.  (Summary)
• H. M. Schey (2005). Div Grad Curl and all that: An informal text on vector calculus. W. W. Norton & Company. ISBN 0-393-92516-1. 
• J.E. Marsden (1976). Vecor Calculus. W. H. Freeman & Company. ISBN 0-7167-0462-5. 

• Chen-To Tai (1995). A historical study of vector analysis. Technical Report RL 915, Radiation Laboratory, University of Michigan.
• Harry F. Davis, Arthur David Snider, Introduction to Vector Analysis, William C Brown Pub; 7 Revised edition (January 1995)

Matrix Analysis

1. Magnus, Jan R., and Heinz Neudecker. Matrix differential calculus with applications in statistics and econometrics. John Wiley & Sons, 2019.

Tensor Analysis

• Bishop, Richard L.; Samuel I. Goldberg (1980). Tensor Analysis on Manifolds, Dover. ISBN 978-0-486-64039-6. 
• Danielson, Donald A. (2003). Vectors and Tensors in Engineering and Physics (2/e ed.), Westview (Perseus). ISBN 978-0-8133-4080-7. 
• Lawden, D. F. (2003). Introduction to Tensor Calculus, Relativity and Cosmology (3/e ed.), Dover. ISBN 978-0-486-42540-5. 
• Lebedev, Leonid P.; Michael J. Cloud (2003). Tensor Analysis, World Scientific. ISBN 978-981-238-360-0. 
• Lovelock, David; Hanno Rund (1989). Tensors, Differential Forms, and Variational Principles, Dover. ISBN 978-0-486-65840-7.