When and where did the switch from a 12 month lunar to a 13 month calendar take place in history and why?

There have been numerous calendars over the years. The Islamic year still consists of twelve lunar months (354 days), and as such their festivals move around the year. The Jewish calendar is lunasolar, being based around solar and lunar dates. Christianity has favoured the Julian and the Gregorian calendars - Gregorian being more accurately aligned to the solstices and equinoxes. Britain adopted the Gregorian in 1752, but Russia still used the Julian until after the Revolution, which is why the "October Revolution" took place in November (European dates). French changed their calendar completely after Revolution in 1789, but reverted to the Gregorian after a few years.

Since Brussells has been attempting to force the return of a 13 month calendar you may see it for yourself.

Try gregorian