In this chapter, we focus on the ten most studied graph convexity parameters, listed in Sect. 2.2 . There is a subsection to each of them where we recall their definition, list results from the literature, and show examples for simple graphs, determining their values in the most known convexities: geodesic, monophonic, and \(P_3\) . Remember that the geodesic, monophonic, and \(P_3\) convexities are associated with minimum paths, induced paths, and \(P_3\) paths within the graph, respectively. As in Lemma 2.3 , they can coincide in certain graph classes, such as the geodesic and monophonic convexities in distance–hereditary graphs, in trees, and in the graph of Fig. 3.2.