The Madsen is a light machine gun that Julius A. Rasmussen and Theodor Schouboe designed and proposed for adoption by Colonel Vilhelm Herman Oluf Madsen, the Danish Minister of War, and that the Royal Danish Army adopted in 1902. It was the world's first true light machine gun produced in quantity and Madsen was able to sell it in 12 calibres to over 34 countries. The gun saw extensive combat usage for over 100 years, with continued use in limited quantities worldwide into the 2010s. The Madsen was produced by Compagnie Madsen A/S (later operating as Dansk Rekyl Riffel Syndikat A/S and then Dansk Industri Syndikat A/S).

The design dates to 1880s, with the Danish Self Loading rifle M.1888 (Forsøgsrekylgevær; lit. 'trial recoil rifle'), being a precursor design. In 1883 Captain Vilhelm Herman Oluf Madsen (a Danish artillery officer), and Rustmester Alexander Bjarnov [da] (a weapons technician at the Danish Arsenal), began working on a recoil-operated self-loading rifle; Madsen developed the idea and Rasmussen fabricated the actual weapons. The rifle used a non-removable stripper clip that used gravity to feed rounds to the action; when the gun was not in use one could fold the clip down to cover the opening. The rifle used the 8×58RD cartridge, first in black-powder and then in a much more powerful smokeless powder version. The design was not successful. An improved design in 1896 gave the rifle an enclosed, but still gravity-fed, magazine. This version saw some 50–60 rifles being produced, but they were only issued to the Danish navy for use by coastal fortifications troops.

Investors formed a company (the Dansk Riffel Syndikat; DRS), in 1898 to commercialise the rifle, and bought the patent rights from Madsen and Rasmussen in exchange for royalties on future production. By this time Madsen had left the project to become Minister of War in Denmark. In 1899 Lieutenant Jens Schouboe became the manager for the DRS, and a number of subsequent patents bear his name. Consequently, the Madsen rifle is sometimes referred to as the Schouboe rifle. In 1901 he patented the design for the Madsen machine gun. The original Madsen machine guns used black-powder cartridges that quickly jammed the action. However, once the design was tried with 6.5mm smokeless powder rounds it worked well.

The Madsen has a rather sophisticated and unique operating cycle. The machine gun uses a mixed recoil-operated locking system with a hinged bolt that is patterned after the lever-action Peabody Martini breechblock. The recoil operation is part short and part long recoil. After firing a round to start the open bolt firing cycle, the initial recoil impulse drives the barrel, barrel extension, and bolt to the rear. A pin on the right side of the bolt moves backward in grooves in an operating cam plate mounted to the right side of the receiver. After 12.7 mm (0.5 in) of travel, the bolt is cammed upward, away from the breech (the "short" portion of the recoil system). The barrel and barrel extension continue to move rearward to a point slightly exceeding the combined overall length of the cartridge case and projectile (the long portion of the recoil system, responsible for the weapon's low rate of fire).

After the breech is exposed, an odd lever-type extractor/ejector, mounted under the barrel, pivots to the rear, extracts the empty case, and ejects it through the bottom of the receiver. The bolt's operating cam then forces the bolt face to pivot downward, aligning a cartridge feed groove in the left side of the bolt with the chamber. While the bolt and barrel are returning forward, a cartridge-rammer lever, mounted on the barrel extension, pivots forward, loading a fresh cartridge.

The Madsen was considered expensive to produce, but was known for its reliability. Thirty-four countries bought the gun, in a dozen different calibres, before and after World War I. Mexico imported 100 Madsens by 1911, some of these being RexersThey were used by all sides of the Mexican Revolution.

In Britain, the Rexer Arms Company manufactured the Madsen with license from 1905 till 1907 The guns were known as the Rexer or DDRS and exported worldwide. However their license was only for sale in Britain and the Commonwealth. Due to this DRS would sue them causing Rexer to dissolve, with most of it‘s assets ending up in the hands of DRS.

The Imperial Russian Army bought 1,250 Madsens for the cavalry and deployed them during the Russo-Japanese War and WW1 The Imperial Russian Air Service used some of these Madsens to equip their Morane-Saulnier G and Morane-Saulnier L monoplanes, and as its open bolt firing cycle made it difficult to fire through a propeller, the Madsen's gun mounting had to fire over the propeller. The German Army deployed the Madsen in 7.92 mm calibre in 1915; having intercepted a shipment of 660 guns originally destined for Bulgaria in 7x57 Mauser and smuggling about 300 guns in 7.62x54R out of Denmark, they would promptly convert them. It would arm infantry companies in defensive formations. Later selling them to Austria-Hungary between 1915 and 16, who would exclusivly use them on the isonzo front. Small numbers were also used by the Belgians, British and Italians forces.