This paper introduces a class of interatomic potential models, called Gaussian Approximation Potentials (GAP), that can be automatically generated from quantum mechanical data on atomic energies and forces. These models do not have a fixed functional form and can model complex potential energy landscapes. They are systematically improvable with more data and are particularly useful for bulk crystals and high-temperature calculations. The method uses a Gaussian Process (GP) regression to interpolate atomic energy in a truncated bispectrum space, enabling efficient and accurate modeling of atomic interactions. The models are tested on bulk semiconductors and iron, showing remarkable accuracy in matching the ab initio potential energy surface at a fraction of the cost. The GAP model outperforms existing potentials in terms of accuracy, particularly in predicting elastic constants and phonon spectra. It is also shown to be effective in modeling complex systems like gallium nitride, where long-range Coulomb interactions are significant. The model includes an Ewald sum of fixed charges to account for these interactions. The GAP model is significantly faster than standard plane-wave DFT codes but more expensive than simple analytical potentials. It is capable of handling large systems and is used to generate long molecular dynamics trajectories, reducing computational cost by orders of magnitude. The model is also extended to multi-component and charged systems by augmenting the local energy with a simple Coulomb term. The authors conclude that the GAP model demonstrates the fundamental capabilities of the method, with potential for further expansion to create "general" interatomic potentials for one- and two-component materials whose accuracy approaches that of quantum mechanics.This paper introduces a class of interatomic potential models, called Gaussian Approximation Potentials (GAP), that can be automatically generated from quantum mechanical data on atomic energies and forces. These models do not have a fixed functional form and can model complex potential energy landscapes. They are systematically improvable with more data and are particularly useful for bulk crystals and high-temperature calculations. The method uses a Gaussian Process (GP) regression to interpolate atomic energy in a truncated bispectrum space, enabling efficient and accurate modeling of atomic interactions. The models are tested on bulk semiconductors and iron, showing remarkable accuracy in matching the ab initio potential energy surface at a fraction of the cost. The GAP model outperforms existing potentials in terms of accuracy, particularly in predicting elastic constants and phonon spectra. It is also shown to be effective in modeling complex systems like gallium nitride, where long-range Coulomb interactions are significant. The model includes an Ewald sum of fixed charges to account for these interactions. The GAP model is significantly faster than standard plane-wave DFT codes but more expensive than simple analytical potentials. It is capable of handling large systems and is used to generate long molecular dynamics trajectories, reducing computational cost by orders of magnitude. The model is also extended to multi-component and charged systems by augmenting the local energy with a simple Coulomb term. The authors conclude that the GAP model demonstrates the fundamental capabilities of the method, with potential for further expansion to create "general" interatomic potentials for one- and two-component materials whose accuracy approaches that of quantum mechanics.