A battle axe is an axe specifically designed as a weapon. Battle axes are essentially specialized versions of utility axes. Many are suitable for use single handedly and others so large that they were wielded two-handed. Axes designed for war range in weight from just over 1lb to 6lbs, and in length from just over a foot to upwards of five feet.
Stone axes have been in use since at least the 3rd millennium BC, see Battle-axe people (see also Mjollnir).
In the eastern Mediterrean the double-bladed labrys was known, and the sagaris, described sometimes as single-bladed, sometimes as double-bladed, became associated with the Amazons. This led Renaissance historians (e.g. Johannes Aventinus) to credit the Amazons with the invention of the battle-axe.
Battle axes were also common in Northern Europe in the "Viking Age" (9th and 10th C) and up to the 16 Century, see Viking Age arms and armour.
The term battle axe applies only to axes used in war. Most medieval European battle axes had broad, socketed heads (meaning the axe head and the haft fit together, rather than lashed together), and some included langets along the haft to prevent the haft from snapping during battle.
In Napoleonic times and later, Farriers in military service carried heavy long axes. Though these could be used for fighting, their primary use was to remove the branded hooves of horses, which were used to prove the deaths of the animals.