Before revision:  The paper starts with explaining mathematical basics that Gaussian processes built on including multivariate normal distribution, kernels, non-parametric models, joint and conditional probability . The Gaussian processes regression is then described in an accessible way by balancing showing unnecessary mathematical derivation steps and missing key conclusive results. An illustrative implementation of a standard Gaussian processes regression algorithmis provided . Beyond the standard Gaussian processes regression, existing software packages to implement state-of-the-art Gaussian processes algorithms are reviewed.
After revision:  The paper starts with explaining mathematical basics that Gaussian processes built on including multivariate normal distribution, kernels, non-parametric models, joint and conditional probability were explained first. Next, the GPR was described concisely together with an implementation of a standard Gaussian processes regression algorithmis provided . Beyond the standard Gaussian processes regression, existing software packages to implement state-of-the-art Gaussian processes algorithms are reviewed.