This is reproduction WW2 American GI side cap
Apparently GI originally meant military equipment made from galvanised iron in WW1, but eventually became anything that was army general issue or government issue and on from that became a word to describe a soldier from the United States of America.
This cap sport 3 stars which means I'm a commander.
This style of hat in the US can also be known as a Campaign cap, flight cap, garrison hat, fore-and-aft cap, envelope cap, overseas cap. It also has some less polite names one being piss-cutter.
