The 13th International Conference “Markov Readings” was held on 15 May 2015 in Moscow. It is an annual event on topical issues of fundamental and applied physics dedicated to the memory and scientific heritage of the outstanding Russian scientist and promoter of science Academician Moisej Aleksandrovich Markov. “Markov Readings” were organized in 2003 and have been held since by the RAS Institute for Nuclear Research, the Lebedev Physics Institute of RAS, the Konstantinov Institute for Nuclear Physics of St.Petersburg and the Joint Institute for Nuclear Research. Academician Moisej Aleksandrovich Markov (1908-1994) is a famous Russian scientist, an outstanding theoretical physicist and promoter of science. He made pioneering contributions to research in neutrino physics, studies of fundamental problems in elementary particle physics, in quantum gravity and at the boundary of particle physics and cosmology. M.A. Markov was the Academician Secretary of the Nuclear Physics Division of the Academy of Sciences of the USSR (1967-1988). In 2002, the Academician M.A. Markov Prize was established by the Institute for Nuclear Research of the Russian Academy of Sciences in commemoration of Academician M.A. Markov who was one of the founders of INR RAS.In the frames of the Conference and according to the decision of the Scientific Council of INR RAS, the Markov Prize’2015 was ceremonially presented to V.A.Matveev – Director of JINR, Full Member of the Russian Academy of Sciences, “for contribution into strong interactions theory and quark model of hadrons”. V.A.Matveev is an outstanding physicist and science organizer; he played a key role in the establishment of hadron quark structure; he is a co-author of the theory of theory of electromagnetic and weak decays of mesons and baryons where electromagnetic mass splitting in isotopic hadron multiplets was explained and mass formulas for higher-order hadron resonances were received. V.A.Matveev made a significant contribution into relativistic approach for coupled particle systems description in the quantum field theory and quantum-field description of particle dispersion at high energies. He is a co-author of the automodelity principle in the high energy physics, the unified approach for description of scale-invariant behavior of deep non-elastic and inclusive processes and widely known rules of Matveev-Muradyan-Tavkhelidze quark counting. He put forward a concept of hidden color of nuclei and showed the significance of quark degrees of freedom for understanding nuclear structure at small distances and predicted baryon matter instability at super high density. Now his scientific interest deals with the elaboration of a program on search for super symmetry on the Large Hadron Collider. In the photo: Academician Valery Rubakov, a co-chairman of the Markov Readings; Academician Victor Matveev, the laureate of the Markov Prize of 2015, director of JINR; Leonid Kravchuk, director of INR RAS.