Nuclear rings are in most cases thought to be by-products of gas shock-focusing at Inner Lindblad Resonances (ILRs). AINUR (Atlas of Images of NUclear Rings) is an Atlas which includes images and metric measurements of all 109 known nuclear rings. This Atlas has been produced by checking and processing Hubble Space Telescope archive data from a complete sample of 488 galaxies. We made structure maps, Halpha and Paschen alpha continuum-subtracted images, and color-index maps in order to detect as many nuclear rings as possible. A few more nuclear rings have been added from a literature search. The 109 nuclear rings are found in 103 galaxies, six of which are elliptical galaxies, five are highly inclined disc galaxies, 17 are unbarred disc galaxies and 75 are barred disc galaxies. We find that dust nuclear rings are found in 6+-2% of elliptical galaxies and that star-forming nuclear rings occur in 19+-% of the disc galaxies with types ranging from T=-3 to T=7. The peak of the star-forming nuclear ring distribution is found between Sab and Sb. The star-forming nuclear ring ellipticities are between 0 and 0.4 assuming that the rings lie in the same plane as the galaxy disc. The maximum possible radius for a nuclear ring in a barred galaxy is a quarter of the bar length. We find that the maximum possible relative size of a star-forming nuclear ring is inversely proportional to the non-axisymmetric torque parameter (``stronger bars host smaller rings'') and that the origin of nuclear rings, even the ones in non-barred hosts, is closely linked to the existence of dynamical resonances. We discuss implications for the lifetimes of nuclear rings and for the evolution of both the rings and their host galaxies. Support by Ministerio de Educacion y Ciencia and Instituto de Astrofisica de Canarias is acknowledged.