The mountain dulcimer originates in rural Appalachia sometime in the early 19th century.  Precise ancestry is unclear, but the German scheitholt seems to be the closest antecedent
Traditionally, mountain dulcimers were built by individual craftsmen, often using local woods and improvised methods.
Scheitholt
Tennessee Music Box
ca. 1890

The builders' craft evolved over time into a fine art.  Since the mid-19th century, tear-drop and hourglass shapes have become the most common, but other configurations are also made. Factory-built mountain dulcimers are now widely available.
Appalachian Mountain Dulcimers
Contemporary dulcimers retain two defining characteristics:
        1.  Diatonic frets
        2. Three strings 
Even these are subject to variations: e.g.,  extra fret(s) or a fourth string doubling the third. 

Still, these two characteristics together preserve the essential heritage of an easily played instrument that anyone can learn.
Stick Dulcimers

In the 1980's stick dulcimers appeared, retaining the traditional limited frets and strings, but held and played guitar-style.