Russia (or the USSR, for these purposes) had an early self-loading rifle in the 1916 Federov, but it was not a satisfactory combat weapons, for several reasons. The Soviet military held a number of trials for a new automatic rifle in the late 1920s and 1930s, and the winner was the Automaticheskaya Vintovka Simonova obraztsa 1936 goda, or Simonov Automatic Rifle, model of 1936. The weapon was adopted as the AVS-36, and put into production. However, it was quickly realized that the design was not a particularly good one. It was complex and expensive to manufacture and prone to malfunctioning in the field. Another trial was held in 1938 between an updated version of the AVS, a rifle designed by Tokarev, and one by a designer named Rukavishnikov. In this trial (and probably with the help of some political intrigue), the Tokarev design won out, and was adopted as the SVT-38.
The AVS-36 was made in relatively small numbers (35,000-65,000, depending on which source you want to believe) and saw use primarily in the Winter War between Finland and the USSR. At the end of that conflict, most of the rifles were collected up and warehoused, to be destroyed by 1943/44. A decent number were captured by Finnish forces and survived that way. The Finnish military was not particularly impressed with the design, but it was popular with some Finnish soldiers.
Functionally, the AVS-36 is a short-stroke gas operated action, with a locking block that slides vertically up and down in the receiver to lock and unlock. The gas system is very similar to the SVT-38/40, but the locking is quite different.
The AVS-36 is most easily recognized by its large and distinctive muzzle brake, which was actually not all that effective. It used a 15-round magazine, and could fire in either semi or full automatic mode. In full auto, it ran at about 800 rounds/minute and was basically uncontrollable (it is not coincidental that it replacement, the SVT-38, was made in semiauto only). A small number of sniper variants of the AVS-36 were made, using a scope mounted off to the left of the bore (to not interfere with the design’s clip loading and upward ejection).
Photos of an AVS-36 (click to download in high resolution):
Photos of an AVS-36 magazine (click to download in high resolution):
You can find an excellent series of photos showing disassembly of an AVS-36 in this thread at guns.ru.