  This text grew out of my lecture notes for a 4-hours minicourse delivered on
October 17 \& 19, 2016 during the research school "Applications of Ergodic
Theory in Number Theory" -- an activity related to the Jean-Molet Chair project
of Mariusz Lema\'nczyk and S\'ebastien Ferenczi -- realized at CIRM, Marseille,
France. The subject of this text is the same of my minicourse, namely, the
structure of the so-called Lagrange and Markov spectra (with an special
emphasis on a recent theorem of C. G. Moreira).
