Guido Tonelli explains how elementary particles, which make up matter, combine into bizarre shapes to form correlated quantum states, primordial soups of quarks and gluons, or massive neutron stars. New questions that have emerged from the most recent research are answered: in what sense is the vacuum a material state? Why can space-time also vibrate and oscillate? Can elementary grains of space and time exist? What forms does matter assume inside large black holes?