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, metric graph, Zhang-Arakelov measure, Berkovich space, (archimedean and non-archimedean) Green's function, asymptotic (mixed) Hodge theory, tropical jacobian, tropical polarized abelian variety, tropical theta function, tropical limit, Abel-Jacobi map, tautological cycle, height jump, biextension, Néron model, Zhang-Kawazumi invariant, Faltings delta-invariant, Chern-Weil theory, (archimedean and non-archimedean) pluripotential theory, b-divisor.