The Shapley Concentration is the richest supercluster of clusters in the nearby universe and its core is a remarkable complex formed by the ACO clusters A3558, A3562 and A3556, and by the two minor groups SC 1327-312 and SC 1329-314. This structure has been studied in various wavelength bands, revealing that it is probably dynamically very active. In this paper we present 174 new galaxy redshifts in this cluster complex, which are added to the sample of 540 already existing velocities. The large number of redshifts permits a more accurate and robust analysis of the dynamical parameters of the clusters. In particular, we discuss the complex velocity distribution of A3558, the bimodal distribution of A3556 and SC 1329-313, and calculate the mean velocity and velocity dispersion of A3562. Moreover, for the three ACO clusters we derive the luminosity functions adopting a new fitting technique, which takes into account the galaxy density profiles. Comment: 15 pages, LaTeX with 13 encapsulated postscript figures; MNRAS in press