Secular Evolution of Disc Galaxies and of their Components

8 pages, 4 figures, invited talk, in "Mapping the Galaxy and Nearby Galaxies," Ishigaki Japan, June 2006, eds. K. Wada & F. CombesI discuss several aspects of secular evolution linked to bars and to boxy/peanut bulges, based on a very large number of high resolution, fully self-consistent $N$-body simulations. When the bar forms, it is as thin as the disc. Its three-dimensional shape, however, evolves, so that, at later times, it has a thick inner part and a thin, more extended outer part. The former, when viewed edge-on, is called a boxy/peanut bulge, because of its shape. The strength of the box/peanut correlates with the bar strength, the strongest cases having formed after two buckling episodes. The extent of the box/peanut is considerably shorter than the bar length, in good agreement with orbital structure studies and with observations. Viewed at an angle near to, but not quite edge-on, barred galaxies show specific isodensity/isophotal shapes, which are different in the thick and in the thin part of the bar. The isophotes of M31 also have such shapes. This, taken together with radial photometric profiles and kinematics, argue that M31 is a barred galaxy. Thus, the pseudo-ring seen at roughly 50' could be an outer ring formed at the outer Lindblad resonance of the bar