The article analyzes the concepts of “mass”, “rest mass”, “relativistic mass”, “energy” and considers their content in accordance with modern scientific ideas. An analysis of the specified concepts in physics textbooks and their correspondence to modern scientific theories ‒ special relativity and quantum theory ‒ was carried out. Based on the analysis of the scientific literature, it is shown that according to Minkovskyʼs formalism, mass is a scalar quantity that depends on the 4-vector momentum, and therefore does not depend on the choice of reference system. The introduction of the concept of relativistic mass and the functional relationship between mass and speed is unjustified. In the teaching methodology of physics, it is necessary to take into account the specified features, since in textbooks there is an incorrect or inaccurate description of the concepts “rest mass”, “rest energy”, “total energy” and the connection of rest energy with the speed of light in a vacuum. These concepts play an important role in the formation of a scientific picture of the world in lyceum students.In most studies, despite their scientific value and practical significance for the methodology of teaching physics and natural sciences in general, insufficient attention is paid to the formation of fundamental concepts that are the basis of relevant physical theories. The analysis of modern programs and textbooks shows that the system of physical concepts in the school course consists mainly of fundamental concepts, the formation of which occurs throughout the course of physics taught in gymnasiums and lyceums. The level of formation of these concepts should correspond to the current level of their interpretation in science. However, the structuring of the educational material only in general terms repeats the structure of physical science, as it takes into account the didactic aspect of physical knowledge.
 Keywords: scientific picture of the world; special theory of relativity; quantum theory; mass; energy; momentum; rest mass; rest energy; relativistic mass.