This lecture introduces the concept of segments on a line, defining them as the set of points between two distinct points A and B on a line. It also explains the notation for segments and half-lines, and delves into the axioms governing the relation 'being between' points. Furthermore, it explores how a point on a line divides it into two half-lines, and extends this idea to the separation of a plane by a line into two distinct parts known as half-planes.