The short-sleeved leather jacket that men commonly wore during the 16th and 17th centuries was called a jerkin. If you're dressing up for a Renaissance Faire, you might want to wear a jerkin, along with your doublet and tights.
Jerkins, snug-fitting, light-colored leather jackets, were often decorated by being cut in slashes or punched with holes. Portraits of Renaissance era men often show them in a doublet, a padded shirt or jacket, topped by a jerkin. In the 20th century, the jerkin made a comeback in the British military during both the first and second World Wars, though it was lined with wool to provide extra warmth to soldiers.