Complex analysis

Complex analysis is the area of mathematical analysis that looks at functions on the complex numbers. It has a wide range of uses, including algebraic geometry and analytic number theory, and areas of physics, such as string theory and quantum mechanics. Augustin-Louis Cauchy is normally credited with founding complex analysis, building on the work of Gauss and Euler. Other mathematicians that made significant advances in this field include Riemann, Weierstrass, Kiyoshi Oka and Lars Ahlfors.

Further reading
 Ablowitz, M. J. & Fokas, A. S. (2003). Complex variables: introduction and applications. Cambridge University Press.
 Ahlfors, L. V. (1966). Complex analysis: an introduction to the theory of analytic functions of one complex variable (Vol. 2). New York: McGraw-Hill.
 Shabat, B. V. (1992). Introduction to complex analysis: functions of several variables (Vol. 110). American Mathematical Society.
 Needham, T. (1998). Visual complex analysis. Oxford University Press. | Link to the whole book