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.