EU Visa Question
 

I am planning a four month research trip to the EU next year and will be visiting Sweden, France and other countries. I know a visa is required for visits of more than 90 days to one EU country. I'm wondering that even though I will be in no country for more than 50-60 days, I will be in the EU for approximately 110-120 days. Do I need to obtain a visa? Will multiple visas be required? Should I arrive and leave from the same country and obtain a visa for that country?

EU Visa Question
 

You need to state your nationality to get assistance. For US citizens each country allows up to 90 days free visa stay. If you are going in and out nobody will care but if you are staying within the Schengen zone then contact the consulate of the country you are planning to exit from for further instructions. You may need a Schengen Visa

As a US citizen, you are permitted to stay in the Schengen Zone without a visa for 90 days in any 180 day period. Leaving Schengen and returning will not reset this.

Some countries in the EU are not in the Schengen Zone. Some countries in the Schengen Zone are not in the EU.

If you need a Schengen visa, you should apply to the Schengen country where you will spend most of your time, regardless of where you plan to enter and exit the Schengen Zone. If there is no country where you will spend the bulk of your trip, then you should apply to the country of first entry. Before doing this you should research the requirements for being a long-term visitor.