Americans have a long and proud tradition of exporting their educations system overseas and establishing universities in both Europe and the wider world. You'll find a reasonably comprehensive list of existing overseas American universities and colleges on Wikipedia. US education generally enjoys a very high reputation around the world.

The benefit, to US students considering studying abroad be it for a semester or for their whole undergraduate degree, is that the American universities located in Europe deliver the American style of higher education.
This means that students still complete general education requirements (take a look at AUR's Gen. Ed. program - we're very proud of it) and take courses in your major or specialty. This is different from the average European universitiy, which tend to have less flexibility around course selection and a more rigid program structure.

Also, classes at American universities overseas are taught entirely in English, which means you can be confident of moving forward with your studies and also enjoying a new country or city before you are fluent in another language.

And of course, the majority of American universities in Europe are accredited in the United States - which means you can transfer the credits from your classes here to a US-based institution with ease.  will easily transfer to a domestic university. When considering an American university abroad, one important factor to consider is whether or not the university is accredited in the US. This means that the school’s legitimacy and quality have been tested and verified. Accredited universities generally carry a better reputation than unaccredited ones when applying to graduate schools and for jobs, which is important if you plan to continue studying or working in the US.