This chapter documents the statement that not only the surface has the essential role of demarcation of a finite body, but when it comes to the description of a constituent particle of a material structure, it plays a fundamental theoretical part, which we have to consider more closely. The particle sets a local reference frame for the surrounding space, first of all by an ideal fixed point the origin with respect to which we reckon the directions in that space. The affine differential theory of surfaces is suggested by the very idea of reference frame, and the fixed point serving as its origin, which can also serve as a center, for instance as a center of force. Any matter structure is theoretically thought in terms of particles. The experience shows that such particles are by no means “elementary”, but they exhibit themselves a structure in concordance with the matter structure to which they momentarily belong.