Multiple parton interactions at the LHC Many high energy collider experiments (including the current Large Hadron Collider at CERN) involve the collision of hadrons. Hadrons are composite particles consisting of partons (quarks and gluons) and this means that in any hadron hadron collision there will typically be multiple collisions of the constituents i.e. multiple parton interactions (MPI). Understanding the nature of the MPI is important in terms of searching for new physics in the products of the scatters and also in its own right to gain a greater understanding of hadron structure. This book aims at providing a pedagogical introduction and a comprehensive review of different research lines linked by an involvement of MPI phenomena. It is written by pioneers as well as young leading scientists and reviews both experimental findings and theoretical developments discussing also the remaining open issues DPS theory overview M. Diehl and J.R. Gaunt DPS inclusive and exclusive cross sections sum rules D. Treleani and G. Calucci DPS correlations T. Kasemets and S. Scopetta Multiparton pp and pA collisions from geometry to parton parton correlations B. Blok and M. Strikman DPS phenomenology of final states with jets P.Gunnellini DPS phenomenology of final states with massive vector bosons O. Gueta DPS phenomenology of final states with heavy quarks I. Belyaev and D. Savrina Double triple and n parton scatterings in high energy proton & nuclear collisions D. dEnterria and A. Snigirev The development of MPI modelling in PYTHIA T. Sjöstrand Measurement of the observables sensitive to underlying event S. Bansal R.D. Field and D. Kar Phenomenology of soft QCD: the role of minimum bias measurements J.F. Grosse Oetringhaus Tuning of MC generator MPI models A. Buckley and H. Schulz Multiparton interactions small x processes and diffraction F. Hautmann and H. Jung High multiplicity collisions M. Floris and W. Li Event shapes at hadron colliders A. Ortiz Dipoles in impact parameter space and rapidity G. Gustafson and L. Lönnblad High multiplicity events in p+p collisions from the color glass condensate and Lund string fragmentation P. Tribedy Multiple scattering in EPOS K. Werner et al