I am interested in getting my undergraduate degree in the US but would love to get my PhD in Europe later on. Is it necessary to get a master’s degree before pursuing a PhD in Europe or could I be accepted into programs with only a US undergraduate degree?
Usually for a European PhD, if you don’t have a masters already, you will do a 1 year masters course at the university before starting the (3-4 year) research only PhD. Funding may or may not be available for both. Admission to the PhD may also be contingent on achieving a good performance in the masters.
I wouldn’t specifically seek a US masters that will likely take two years and may be much more expensive than a one year masters in Europe just to qualify you for a PhD, unless your undergrad course grades and other experience are insufficient to get admitted to/funded for the PhD program.
Note that in Europe, funding may be separate from the actual admissions: it is often much easier to get admitted than to get funding.