(Mus musculus). Its scientific name means 'mouse littlemouse'. They don't survive long outdoors, but generally we don't like them indoors. However, you can now put up a device that keeps out unwanted rodents by releasing a sound that repels them. Be careful, though, if you keep pet rodents. You don't want a frenzied guinea-pig on your hands.
In my grandfather's day, trap and cat were the usual devices that drove mice out. My grandfather had other ideas. He used gunpowder until one day he blew out the stairs. My grandmother made him desist from the practice.
In France, tooth fairies are thought to be mice.
The rat is held in even greater distaste by householders. The commoner ones are the black rat (Rattus rattus) and the brown rat (Rattus norvegicus). Both are found worldwide. On shipboard, it is supposedly unlucky to mention a rat and you should use the term longtail instead. The same word is used on the Isle of Man, a British dependency between Britain and Ireland.
The black rat is said to have carried the parasite which brought the Black Death. In the 18th Century the brown rats, migrating across eastern Europe, reached the Baltic and there boarded ships which transported them worldwide. In Britain they proceeded to kill off most of the black rats and there hasn't been a plague there since.
In Ireland, if you needed to get rid of rats, a rat whisperer might be called to your farm. He would use some unknown process to make the rats leave. As he could never be watched while he executed this, no one knows what he did.
If you have a rat in your house, it is said he will leave if you go to the rat hole and simply ask him to. You should suggest while doing so the location of an alternative place of residence. Some people have declared the efficacy of stuffing a written letter into the rat hole, suggesting he leave.
In the London sewers, it is said there is a King Rat, bigger than the other rats and treated by them with deference.
The London sewers in the 19th Century were said to have a Queen Rat, who would turn herself into human form and copulate with toshers, poor folk who went fishing in the sewers. It had no effect on their health, but children they subsequently begot had eyes of different colors.