are Permits required for the installation of a swimming pool, spa, or hot tub?

Depends on the locale and the intended use.

In most all places, permits aren't required for hot tub/spa installations... however if it is inground, it may require one. Some may require electrical permits as well.

Swimming pools, most places do require them for inground installs. Above ground easier to get away with.

That's the way I understand the way of the world.

Insurance companies and some local jurisdictions may want to see fencing and gates so children can't get in without going over fences or through open gates.

Aside from my gas & electircal stuff, this was of the most concern to my inpsector.