Holomorphic Functions

We define holomorphic functions of n complex variables and present the elementary properties. A characteristic caused by increasing the number n of variables more than one is the so-called Hartogs phenomenon in the analytic continuation, such that all holomorphic functions in a domain of Cn (n ≥ 2) are simultaneously analytically continued over a strictly larger domain; such a phenomenon never occurs in one variable. We also prepare some basic notion necessary in the later chapters.