Is it allowed to skip gears with manual transmission?

Is it allowed to skip gears with manual transmission? If you want to save some effort while driving, you might skip a gear, for example, when accelerating on the outskirts of the city, going directly from third to fifth or even sixth gear. But does this harm the engine? Skipping gears when upshifting is not a problem. Nowadays, engines can run smoothly even at low RPMs. At worst, the car might jerk a bit or you might stall the engine and then have to downshift. The real issue is the abrupt downshifting, such as going from fourth to second gear. This can cause the engine to over-rev. Even though the technology in newer cars often prevents this, one should still be cautious when downshifting.