A half-track is a motor vehicle with a hybrid of running gear types. In the rear, for propulsion, a half-track has caterpillar tracks - flexible bands driven by wheels inside the tread loop, most often seen driving tanks. In the front, a half-track has either wheels or skis for ease of steering. This layout has several advantages and some disadvantages over fully-tracked or all-wheeled vehicles. The tracks provide the ability to gain traction over a wide range of surfaces, including steep hills and snow, ice, mud or sand where wheels would become bogged. The front wheels allow for nimble steering without the surface-damaging, mechanically complex and clumsy use of tread braking. Driving skills learnt on wheeled vehicles transfer easily to half-tracks. On the other hand, they are more complex than wheeled vehicles, usually slower, and not as robust as fully-tracked vehicles.
The first half-track was built by a French engineer named Kégresse for Tsar Nicholas II of Russia in 1911. Versions were built in the U.S. to haul cargo over unimproved roads, with the Garford Truck conversion being the first track/wheel unit built and the basis for U.S. World War I models. Canada built some to handle snow; Faster French half-tracks (Citroen-Kégresse autochenilles) were eventually built after 1931 for desert use in Africa. American engineers based the famous World War II M2 and M3 half-track vehicles on these. Germany and Russia also built half-tracks during that war, which saw perhaps the most widespread use of them before tanks became reliable and long-range enough (and wheeled vehicles durable enough) to eclipse their niche.
Recommended reading: "Half-Track: A History of American Semi-Tracked Vehicles" by R.P. Hunnicutt. Novato CA: Presidio Press, 2001.