From the famous formula E = mc², the nuclear mass yields directly the binding energy of a nucleus, i.e. the result of all interacting forces within this nucleus. The Atomic Mass Tables are the fruit of the evaluation of all valid experimental data aiming at mass measurements, or in which relevant energy measurements are given.

In the present course, addressed to university students, there will be first a recall about the nucleus and the nuclear binding energies, exhibiting the most important quantities and what could be learned from them; illustrated by various view of the "Chart of the Nuclides". Then I will show how the knowledge of these energies is important in many domains of physics, from basic research to application to every day’s life. In particular, I will give several examples of discoveries in Nuclear Physics due to our knowledge of the masses: the discovery of isotopes, of shells, of nuclear deformation, and also solving the otherwise intriguing problem of the age of the Sun.

How the masses of the nuclei are measured experimentally will then be reviewed: masses are obtained either as energy measurements through reaction energy measurements and also decay energy measurements; or as an inertial mass, since an ion beam will have its trajectory curved in a magnetic field, with direct relation to its mass. These last ones are often called "Direct" mass measurements, the different types of which I will review, from the historical spectrometer of Thomson in 1907, to the modern Penning traps and storage rings methods. The results of all types of measurements and of all experiments performed in all the laboratories around the world are then combined in order to derive a "list" of recommended mass values, the "Atomic Mass Tables", the most recent version of which has just been published in the Chinese Physics C journal in December 2012, following the 2003 one.