For U.S. citizens, the total length of residence in the Schengen territories without a residence or work permit must not exceed three months (90 days) in any six-month period. You are free to travel in and out of the Schengen area during the six-month period as long as you do not overstay the total 90-day limit. The US State Department publishes information on the Schengen area to which you should refer.