This first paper was aimed at providing the basic formulations of moments, a classification and an introductory bibliography. The moment-based approaches have a number of interesting features. They have a wide range of orthogonal and non-orthogonal basis functions and are simple to compute whatever the order required. The image sampling can be either rectangular or polar, based on uniform or non-uniform lattices. Their optimal choice to deal with a given problem is however not obvious according to the requirements to face. There are of course many other issues to address. Among the important properties to consider there are (i) the invariance to scale, translation, and orientation, etc. (ii) the robustness to degradations, noise, to changing conditions (illumination) or blurring and (iii) to object variations (multiple appearances, occlusions and deformations). Moment computations have also a cost that is sometimes considered too high for certain applications: this explains that a special attention has been devoted to acceleration techniques and VLSI implementations. These important aspects for computer vision at large and the most meaningful works in medical imaging will be examined in the next papers.