Armoured fighting vehicle
Evolution: The concept of a highly mobile and protected fighting unit has been around for centuries; from Hannibal's war elephants to Leonardo's contraptions, military strategists endeavoured to maximize the mobility and survivability of their soldiers.
Armoured fighting vehicles were not possible until internal combustion engines of sufficient power became available at the start of the 20th century.

History: 

Pre-modern: Modern armoured fighting vehicles represent the realization of an ancient concept – that of providing troops with mobile protection and firepower. Armies have deployed war machines and cavalries with rudimentary armour in battle for millennia. Use of these animals and engineering designs sought to achieve a balance between the conflicting paradoxical needs of mobility, firepower and protection.

Siege machine: Siege engines, such as battering rams and siege towers, would often be armoured in order to protect their crews from enemy action. Polyidus of Thessaly developed a very large movable siege tower, the helepolis, as early as 340 BC, and Greek forces used such structures in the Siege of Rhodes (305 BC).
The idea of a protected fighting vehicle has been known since antiquity. Frequently cited is Leonardo da Vinci's 15th-century sketch of a mobile, protected gun-platform; the drawings show a conical, wooden shelter with apertures for cannons around the circumference. The machine was to be mounted on four wheels which would be turned by the crew through a system of hand cranks and cage (or "lantern") gears. Leonardo claimed: "I will build armoured wagons which will be safe and invulnerable to enemy attacks. There will be no obstacle which it cannot overcome." Modern replicas have demonstrated that the human crew would have been able to move it over only short distances.

War wagon: Hussite forces in Bohemia developed war wagons – medieval horse-drawn wagons that doubled as wagon forts – around 1420 during the Hussite Wars. These heavy wagons were given protective sides with firing slits; their heavy firepower came from either a cannon or from a force of hand-gunners and crossbowmen, supported by light cavalry and infantry using pikes and flails. Heavy arquebuses mounted on wagons were called arquebus à croc. These carried a ball of about 3.5 ounces (100 g).

Modern: By the end of World War II, most modern armies had vehicles to carry infantry, artillery and anti-aircraft weaponry. Most modern AFVs are superficially similar in design to their World War II counterparts, but with significantly better armour, weapons, engines, electronics, and suspension. The increase in the capacity of transport aircraft makes possible and practicable the transport of AFVs by air. Many armies are replacing some or all of their traditional heavy vehicles with lighter airmobile versions, often with wheels instead of tracks.

Armed and armoured car: The first modern AFVs were armed cars, dating back virtually to the invention of the motor car. The British inventor F. R. Simms designed and built the Motor Scout in 1898. It was the first armed, petrol-engine powered vehicle ever built. It consisted of a De Dion-Bouton quadracycle with a Maxim machine gun mounted on the front bar. An iron shield offered some protection for the driver from the front, but it lacked all-around protective armour.
The armoured car was the first modern fully armoured fighting vehicle. The first of these was the Simms's Motor War Car, also designed by Simms and built by Vickers, Sons & Maxim in 1899. The vehicle had Vickers armour 6 mm thick and was powered by a four-cylinder 3.3-litre 16 hp Cannstatt Daimler engine giving it a maximum speed of around 9 miles per hour (14 kilometres per hour). The armament, consisting of two Maxim guns, was carried in two turrets with 360° traverse.

Another early armoured car of the period was the French Charron, Girardot et Voigt 1902, presented at the Salon de l'Automobile et du cycle in Brussels, on 8 March 1902. The vehicle was equipped with a Hotchkiss machine gun, and with 7 mm armour for the gunner. Armoured cars were first used in large numbers on both sides during World War I as scouting vehicles.

Tank: In 1903, H. G. Wells published the short story "The Land Ironclads," positing indomitable war machines that would bring a new age of land warfare, the way steam-powered ironclad warships had ended the age of sail.
Wells's literary vision was realized in 1916, when, amidst the pyrrhic standstill of the Great War, the British Landship Committee deployed revolutionary armoured vehicles to break the stalemate.  The tank was envisioned as an armoured machine that could cross ground under fire from machine guns and reply with its own mounted machine guns and naval artillery.  These first British tanks of World War I moved on caterpillar tracks that had substantially lower ground pressure than wheeled vehicles, enabling them to pass the muddy, pocked terrain and slit trenches of the Battle of the Somme.

Troop transport: The tank eventually proved highly successful and, as technology improved, it became a weapon that could cross large distances at much higher speeds than supporting infantry and artillery. The need to provide the units that would fight alongside the tank led to the development of a wide range of specialised AFVs, especially during the Second World War (1939–1945).
The armoured personnel carrier, designed to transport infantry troops to the frontline, emerged towards the end of World War I. During the first actions with tanks, it had become clear that close contact with infantry was essential in order to secure ground won by the tanks. Troops on foot were vulnerable to enemy fire, but they could not be transported in the tank because of the intense heat and noxious atmosphere. In 1917, Lieutenant G. J. Rackham was ordered to design an armoured vehicle that could fight and carry troops or supplies. The Mark IX tank was built by Armstrong, Whitworth & Co., although just three vehicles had been finished at the time of the Armistice in November 1918, and only 34 were built in total.

Tankette: Different tank classifications emerged in the interwar period. The tankette was conceived as a mobile, two-man model, mainly intended for reconnaissance. In 1925, Sir John Carden and Vivian Loyd produced the first such design to be adopted – the Carden Loyd tankette. Tankettes saw use in the Royal Italian Army during the Italian invasion of Ethiopia (1935–1936), the Spanish Civil War (1936–1939), and almost everywhere Italian soldiers fought during World War II. The Imperial Japanese Army used tankettes for jungle warfare.

Self-propelled artillery: The British Gun Carrier Mark I, the first Self-propelled artillery, was fielded in 1917. It was based on the first tank, the British Mark I, and carried a heavy field-gun. The next major advance was the Birch gun (1925), developed for the British motorised warfare experimental brigade (the Experimental Mechanized Force). This mounted a field gun, capable of the usual artillery trajectories and even anti-aircraft use, on a tank chassis.
During World War II, most major military powers developed self-propelled artillery vehicles. These had guns mounted on a tracked chassis (often that of an obsolete or superseded tank) and provided an armoured superstructure to protect the gun and its crew. The first British design, "Bishop", carried the 25 pdr gun-howitzer in an extemporised mounting on a tank chassis that severely limited the gun's performance. It was replaced by the more effective Sexton. The Germans built many lightly armoured self-propelled anti-tank guns using captured French equipment (for example Marder I), their own obsolete light tank chassis (Marder II), or ex-Czech chassis (Marder III). These led to better-protected tank destroyers, built on a medium-tank chassis such as the Jagdpanzer IV or the Jagdpanther.

Anti-aircraft vehicle: The Self-propelled anti-aircraft weapon debuted in WWI. The German 88 mm anti-aircraft gun was truck-mounted and used to great effect against British tanks, and the British QF 3-inch 20 cwt was mounted on trucks for use on the Western Front. Although the Birch gun was a general purpose artillery piece on an armoured tracked chassis, it was capable of elevation for anti-aircraft use. Vickers Armstrong developed one of the first SPAAGs based on the chassis of the Mk.E 6-ton light tank/Dragon Medium Mark IV tractor, mounting a Vickers QF-1 "Pom-Pom" gun of 40 mm. The Germans fielded the Sd.Kfz. 10/4 and 6/2, cargo halftracks mounting single 20 mm or 37 mm AA guns (respectively) by the start of the war.

Self-propelled multiple rocket-launcher: Rocket launchers such as the Soviet Katyusha originated in the late 1930s. The Wehrmacht fielded self-propelled rocket artillery in World War II – the Panzerwerfer and Wurfrahmen 40 equipped half-track armoured fighting vehicles. Many modern multiple rocket launchers are self propelled by either truck or tank chassis.