For a domain in the complex plane, its Bergman, Szegö and Poisson kernels are called simple, if they are not genuine functions of two complex variables, but composed of finitely many holomorphic functions of one variable. This paper announces a proof of the results that in the case of finitely connected domains these kernels are simple. In the case of a bounded finitely connected domain with smooth boundary, all the kernel functions are composed of basic holomorphic functions given as solutions to explicit Kerzman-Stein integral equations, which may be computed quite easily. And only finitely connected domains with Bergman or Poisson kernels being rational functions are the simply connected domains which can be mapped onto the unit disc by a rational biholomorphic mapping. This has as a corollary that the Green's function for a finitely connected domain is \(1/2 \log\)\{rational function\}, if and only if the domain is simply connected and there is a rational biholomorphic mapping of it onto the unit disc.