Do European Shoes Run The Same As My American Size?

No, they do not. As a matter of fact, the difference between a 36 and a 37 is a bit more than an American half size and not quite a full size. This difference, along with the fact that most of these companies only make one width, makes it very difficult to fit as accurately. You may have to accept some fitting limitations along with some adjustments. A professionally trained shoe fitter will explain these issues to you and how the adjustments will need to be done. The fitter, if trustworthy, will also tell you if this could be a problem as you wear the shoes. As more companies convert to the metric sizing, you will have to rely on the professionally trained fitter to fit your foot as proportionally as possible.