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Systema (Russian: ???????, “The System”) is a Russian martial art. It is designed to be highly adaptive and practical, training using drills and sparring instead of set kata. It focuses mainly on controlling the six body levers (elbows, neck, knees, waist, ankles, and shoulders) through pressure point application, striking and weapon applications. Systema is often advertised as being a martial art employed by some Russian Spetsnaz units. 
There is no historical “real name” for these arts. In many cases, it’s common to simply see “Russian martial arts” used, although that can lead to some confusion. In a sense, the name “Systema” (the system) can be thought of as a generic title comparable to “Kung Fu” (“one who is highly skilled” or “time” and “effort”).  The most likely version is that the name Systema was taken from the name given in Russia to a similar martial art before that, the Systema Rukopashnogo Boya (System of hand-to-hand combat).
At least in Mikhail Ryabko’s Systema, “The System” is a reference to the various systems of the body (Muscle, Nervous system, respiratory system, etc) as well as elements of Psychology and the Spirit. 
As there have been and still are a number of different fighting styles common throughout the Russian military and special forces, like Alpha, GRU, Vympel, several other names and nicknames are commonly mistaken for Systema. For example, some troops and special forces personnel train in “boevoe sambo” (combat sambo), which is a separate art. Also, troops would refer to whatever was taught as “rukopashka” (Russian slang for “hand to hand”), or “machalka” or “boinia” (Russian slang for “fighting” and “beating”). The name “Combat Sambo Spetsnaz” was coined by the Soviet government, even though those are different styles.
Joseph Stalin’s personal bodyguards were practitioners of Systema.   Ryabko was taught the system in the army by one of those bodyguards. After Stalin’s death, Systema became the style of fighting employed by some Special Military Operations Units for high risk missions in Spetsnaz, GRU and other government facilities. There were and are a number of different combat arts trained throughout Russian special forces units other than Systema. It is due to the Soviet Union’s strict ban on non-sanctioned traditions, and the sensitivity of special forces training, that it was not until after the cold war that Systema became known. Systema’s pre-Soviet Russian heritage is only recently being rediscovered.
It is likely that the roots of Systema are lost in ancient and family arts, changed by military and contemporary needs and rediscovered and adapted by each instructor and practitioner.
Some claim that Systema’s Russian martial arts heritage dates back to the 10th century and was practiced by the Bogatyr (Russian heroes/knights).   
Another theory proposes that the various forms of modern Systema are evolutions of an intensive research and development project carried out by several generations of hand to hand combat instructors at the Dinamo training facility in Moscow between roughly 1920-1980. If so, that would place Systema in the same stream of military close-combat training as combat SAMBO and related styles such as SAMOZ, which was developed by V.A. Spiridonov. If this theory is correct, the stylistic influences on modern Systema would include numerous national martial arts styles, military close-combat systems and indigenous Russian combat styles as well as aspects of sports science, biomechanics and sports psychology as these disciplines were incorporated into the Dinamo close-combat research and development project during the 20th century.
It has been claimed that one or both of Ryabko and his student Vlad Vasiliev created the art based upon their experiences.
Systema is counted alongside a number of pre-Soviet traditions which are being actively cultivated by the Russian government. In 2004, the Dinamo Sports Center played host to a demonstration and celebration of martial traditions.
It is still a relative unknown, but Systema or relatives to it are being taught by several practitioners inside and outside of Russia. Of particular interest is that different people from different backgrounds were taught subtle variations of Systema.
Furthermore, since practitioners train in their own preferred manner and with their individual understanding, their style expressed in their art is unique to them. This is most readily seen with senior students and other high-level artists.
As some students train to become instructors in their own right, their understanding evolves and they ultimately teach a personal and more contemporary version of their understanding. In some cases this personal understanding keeps the same name, and in some cases a new name is warranted.