This chapter is an introduction to the theory of analytic functions of single
variable. No one can understand the basic concepts of integration without passing
through analytic functions. It will be so difficult starting deeply with such functions but
the reader should first start from the basic definitions and then slowly develop the ideas
of complex analysis to the point that considered the bases to deeper topics such as
Cauchy's theorem and the Riemann mapping theorem.
Keywords: Complex-valued function, domain and range of complex-valued
function, Cauchy theorem, Riemann mapping theorem, mapping, linear
transformation, inverse transformation, bilinear transformation, logarithmic
complex function.
