When most people think of "rodents", they most likely think of rats or mice. This is fair enough, as the great majority of rodent species pretty much fit that description. But there are, of course, many others. Voles, hamsters, gerbils, and so on are probably fairly obvious, and somebody once asked me if squirrels were "members of the vermin family", by which I assume they meant "rodents" - which they certainly are. One suspects, however, that beavers might come fairly low on most people's list.
Having said which, it's probably not so surprising when you think about it. They do, after all, have huge gnawing teeth that look like those of rats (and which, indeed, help define the rodents as a group). Granted, they are pretty enormous as rodents go, and bulky with flat, paddle-shaped tails, but rodents they are, with animals like gophers and kangaroo rats among their closest relatives.
The beaver family, ignoring the extinct forms, contains a grand total of two species, both of which are found in Europe. One of them is the animal familiar to Americans (
Castor canadensis). Descended from a population that originally lived in Wyoming and Canada, these were shipped across to Finland in 1937, and subsequently spread across the country, crossing the eastern border into Russia in 1952. A year later, some of them were moved again, this time to Austria, and in the 1970s, some were shipped all the way to eastern Siberia. All of these populations survive, although attempts to introduce the animals to France, Ukraine, and Belarus all ultimately failed.