I wear an 8.5 -9.0 medium  ( mostly prefer a 9 in structured and athletic shoes and boots) and I ordered the 10 which fit perfectly and I can wear them with or without socks.  I would definitely recommend ordering up a full size for starters  because it's most likely that you will need more room given that they are dancing shoes. They seem to be a medium width with a slight tendency to be more on the narrow side of medium. A person with a truly narrow foot may want to order up only 1/2 size vs. full.  Aside from the size issue, the leather is very soft, pliable and the shoes mold to my feet very well without binding, pinching or rubbing and there is no breaking in needed.  These shoes fit as well as a soft leather glove.  Very nice!  For added reference info, the insole of the size 10 measures right at 10 inches and my foot measures ( big toe to heel)9 7/8 inches. I believe that size 10 equates to a size 40 eur.  Hope that helps