Optical lattices: cold atoms ordered by light

We present here an introduction to optical lattices starting from the basic concepts of laser cooling of neutral atoms. Ordered structures, composed of cold atoms in an interference pattern, are then described, with a particular emphasis on the basic mechanism called Sisyphus cooling. Afterwards, we introduce the basic elements of the main physical problem tan atom moving in a spatially modulated electromagnetic field) and we make a concise description of the various theoretical approaches that have been introduced in the literature in order to solve that problem. Finally, we report a detailed list of the multiple diagnostic tools that have been developed by physicists in order to investigate the static and dynamical properties of these systems. The new developments and the perspectives of the research field on optical lattices are then quickly discussed and conclude this introductory review.