This book describes non-perturbative quantum chromodynamics (QCD) in ways accessible to graduate students and researchers who know some textbook fundamentals of QCD.Although QCD has long been the accepted theory of interactions involving quarks and gluons, there is still controversy over how to explain fundamental non-perturbative aspects such as confinement and chiral symmetry breakdown. This book gives a picture of the leading contender for understanding non-perturbative QCD, through center vortices and their monopole-like partners, called nexuses.It begins where the textbooks finish, first explaining how to do calculations in QCD with the pinch technique, a formalism for calculating gauge-invariant and unambiguous QCD Green's functions. It goes on to show how these techniques lead, beyond perturbation theory, to a kind of gluon mass as indicated by a finite and positive value for the gluon propagator at zero momentum — as unambiguously revealed by computer simulations. It then goes on to show how such a mass leads to a condensate of quantum solitons, called center vortices and nexuses, that are responsible for confinement and other non-perturbative properties of QCD. These solitons are non-linear bound states of gluonic fields that owe their existence to the gluon mass, which self-consistently owes its existence to a spaghetti-like condensate of the solitons. These solitons and their effects are also seen in lattice simulations.