Here, I introduce some nice books that are both in my research interests and general interests in mathematics. You may find them useful for your own study/research. I have tried my best to mention books that I have either studied  (fully/partially) or have had enough familiarity with their contexts.

My research interests

Complex Analysis

• Complex Analysis,  An Introduction to the Theory of Analytic Functions of One Complex Variable, Lars V.  Ahlfors, 1979.

• Functions of One Complex Variable I,  John B.  Conway, 1995.

• Basic Complex Analysis,  Jerrold E.  Marsden, 1998.

• Complex Functions,  An Analytic and Geometric Viewpoint, G.  A.  Jones, D.  Singerman, 1987. 

• Classical Topics in Complex Function Theory, Reinhold Remmert, Springer-Verlag, 1997.  

• Elementary Theory of Analytic Functions of One or Several Complex Variables (Dover Books on Mathematics) by Henri Cartan. 

• An introduction to the theory of the Riemann Zeta-function, S. J. Patterson, Cambridge studies in advanced mathematics, no 14, Cambridge University Press, 1988.

Complex Approximation Theory 

• Lectures on Complex Approximation theory,  D. Gaier, Translated by R. McLaughlin, Birkhäuser, 1985.

• Approximation of Functions, G. G. Lorentz, Chelsea Publishing Company, New York, 2nd Ed, 1986.

Riemann Surfaces

• Riemann Surfaces, L. V. Ahlfors and L. Sario, 1960.

• Riemann Surfaces, Farkas, H. M., Kra, I. 1980.

• Lectures on Riemann Surfaces, Otto. Forster, 1981.

• Geometric Function Theory and Conformal Mappings

• Conformal Invariants, Topics in Geometric Function Theory, Lars V. Ahlfors, 1973.

• Boundary Behaviour of Conformal Maps, Ch. Pommerenke, 1992.

• Geometric Theory of Functions of a Complex Variable, G. M. Goluzin, 1969.

• Conformal Mappings, Zeev Nehari, 1952.

Teichmüller Theory/Spaces

Univalent Functions and Teichmuller Theory, Olli. Lehto, 1986.

Univalent Function Theory

• Univalent Functions, Peter. L. Duren, 1983.

• Univalent Functions, with a Chapter on Quadratic Differentials, Christian Pommerenke and Gerd Jensen, 1974.

• Univalent Functions, Vol I and II, A. W. Goodman, 1983.

Real and Classical Analysis

• Principle of Mathematical Analysis, W. Rudin, 1964.

• Modern Mathematical Analysis, M. H. Protter C. B. Morrey, 1964.

• Real Analysis, H. L. Royden, 1988.

• Understanding Analysis, Stephen Abbot, 2nd Ed, Springer New York, NY. 

• The Logarithmic Integral. Koosis P., Cambridge University Press; 1988. 

History, Philosophy

• Mathematics of the 19th Century: Geometry, Analytic Function Theory, by Andrei N. Kolmogorov, Adolf-Andrei P. Yushkevich, 1996.

About Mathematics/Mathematicians...

• The Way I Remember it, Walter Rudin, 1996.

• A Mathematician's Apology, G. H. Hardy, 1940.

• The Scottish Book, R. Daniel Mauldin, 2nd Ed, 2015.

• Uncle Petros and Goldbach's Conjecture: A Novel of Mathematical Obsession, Apostolos Doxiadis, 2001.

• Letters to a Young Mathematician, Lan Stewart, 2006.

• Birth of a Theorem, Cédric Villani, 2011.

• Gödel's Theorem: An Incomplete Guide to Its Use and Abuse. Torkel Franzén, 2005.