Keywords and themes are: arithmetic intersection theory, theta divisor, Faltings height, self-intersection of the relative dualising sheaf, admissible pairing, Gross-Schoen cycle, Mahler measure, equidistribution, Bogomolov conjecture, Beilinson-Bloch height, Berkovich space, (archimedean and non-archimedean) Green's function, asymptotic (mixed) Hodge theory, tropical jacobian, tropical theta function, tautological cycle, height jumping, biextension, Néron model.