This paper is devoted to the study of Markov kernels on general measurable space under first-order minorization condition and modulated drift condition. The following issues can be addressed: Existence and uniqueness of invariant measures, recurrence/transience properties including Harris-recurrence property, convergence in total variation of iterates, Poisson's equation, perturbation schemes and rate of convergence of iterates including the so-called geometric ergodicity. All theses issues are discussed in the present document except the perturbation schemes and the non-geometric rate of convergence of iterates, both which will be included soon to form our final text. All the results reported here focus on Markov kernels using a residual kernel approach. This turns out to be a very simple and efficient way to deal with all mentioned issues on Markov kernels. In particular, the document is essentially self-contained.