First let us go back a few centuries in time and study how infantry warfare worked in the 1600s, 1700s and part of the 1800s. Back in those days, most firearms were smoothbore muskets, such as the famous Brown Bess, which was in service with the British military for over 100 years. Since muskets had no rifling, accuracy was somewhat limited. Also, since these firearms were muzzle loaders using mostly flintlock firing mechanisms, they were slow to load and use. Therefore the standard military strategy of the day was to line up three lines of troops about 50-100 meters away from the enemy. The first line would fire their weapons and immediately retreat to the rear. The second line would then step forward and in turn discharge the weapons and then retreat to the rear and the third line would repeat the same process. Meanwhile, this would hopefully give the first line enough time to reload their firearms so they could fire another volley. Each line was coordinated by an officer so that all the men in one line would fire at approximately the same time. This strategy also maximized the firepower of the unit. Since the firearms weren't very accurate, it was hoped that the massed fire would hit at least some of the enemy troops. In fact, Colonel George Hanger of the British Army famously said, "A soldier's musket, if not exceedingly ill-bored (as many are), will strike a figure of a man at 80 yards; it may even at a hundred; but a soldier must be very unfortunate indeed who shall be wounded by a common musket at 150 yards, providing his antagonist aims at him; and as to firing at a man at 200 yards with a common musket, you may as well fire at the moon and have the same hope of hitting him. I do maintain and will prove…that no man was ever killed at 200 yards, by a common musket, by the person who aimed at him."
In the 1800s, with the advent of rifled firearms, massed fire tactics and tight formations began to fade away. As accuracy was improved, it was no longer practical for soldiers to fire at each other from standing positions over a plain. It took a while for military planners to realize that massed fire tactics were obsolete though, as can be witnessed by the huge casualties in the American Civil War, where men still shot at each other in tight formations at distances less than 100 yards apart. The final death knell of the massed formation strategy came in World War I, where the machine gun, trenches and artillery rendered this method obsolete. Instead, troops took pot shots at each other from longer ranges and from trenches.
In 1890, an Italian officer named Amerigo Cei-Rigotti invented an rifle, which was capable of selective fire (single shots or burst mode). The rifle was designed to fire 6.5x52 mm. ammunition from a detachable magazine. Incremental modifications were made to the rifle until 1900 before it was dropped from consideration. While this was the first real "assault" rifle, it wasn't very popular because it was extremely unreliable and had a very high rate of misfiring and jamming. That is why it was never adopted by any military anywhere.
The next development was the Fedorov Avtomat from Russia, in 1916. This particular firearm was developed by Vladimir Fedorov. This firearm was relatively lighter weight than other firearms of its time, had a large detachable magazine, had capability to switch firing mode from single shot to automatic mode and used an intermediate powered cartridge (smaller than a rifle cartridge, but larger than a pistol cartridge). The cartridge used for this was originally a custom designed 6.5 mm. cartridge, but it was later switched to use a 6.5x50 mm. Japanese designed Arisaka cartridge because it was available in quantity already. While this cartridge appears big compared to modern cartridges, remember that ammunition was not as powerful in those days, so it could be considered as an intermediate power cartridge. The Fedorov Avtomat was not produced in great numbers, but it was popular with Russian troops until World War II.
Federov avtomat assault rifle. Click on image to enlarge. Image is in the public domain.
The Fedorov Avtomat was influential because it was the first practical assault rifle that was adopted by a military anywhere. Incidentally, its inventor, Colonel Fedorov, also invented the concept of the infantry weapon family, where carbine, assault rifle, light machine gun, medium machine gun etc. would all share some commonality of parts (e.g.) action, receiver, trigger assembly etc.