The aim of this paper is to present a unified framework in the setting of Hilbert C∗-modules for the scalar- and vector-valued reproducing kernel Hilbert spaces and C∗-valued reproducing kernel spaces. We investigate conditionally negative definite kernels with values in the C∗-algebra of adjointable operators acting on a Hilbert C∗-module. In addition, we show that there exists a two-sided connection between positive definite kernels and reproducing kernel Hilbert C∗-modules. Furthermore, we explore some conditions under which a function is in the reproducing kernel module and present an interpolation theorem. Moreover, we study some basic properties of the so-called relative reproducing kernel Hilbert C∗-modules and give a characterization of dual modules. Among other things, we prove that every conditionally negative definite kernel gives us a reproducing kernel Hilbert C∗-module and a certain map. Several examples illustrate our investigation.

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