A short summarized bit of history for those unfamiliar with the weapon:

The Sturmgewehr 44 (german for storm/assault rifle) was the world's first widely used assault rifle. Germans realized that combat more frequently happened in the range of up to 800m, so that the long range of the 8mm Mauser cartridge was unnecessary for general combat, and its high recoil made fully automatic fire unwieldy. An intermediate cartridge would allow for a role between bolt action rifles, like the Kar98K, and submachineguns, like the MP40. Thus began the development of the 7.92x33/8mm Kurz (8mm short) and the Sturmgewehr (at the time Maschinenkarabiner). The weapon was well received by german troops, but had trouble in its development caused by administrative complications: Hitler did not agree with the need for a new rifle and an intermediate cartridge, though he allowed the project to continue as a new submachine gun - which it did, but only in name (Maschinenpistole 43/44). Later, seeing the acclaim for the "new rifle" and its performance, Hitler was impressed, and according to the legend he named it Sturmgewehr.
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A billion years in the making, and it's coming to your galaxy, this summer.

Video by Hodilton:


Features (updated for version 1.2):
3 barrels: standard, long and short.
6 stocks: Full, folding, folded, +alternate handguard versions of all.
15 receivers
5 magazines: standard, standard quick, short, short quick, and drum.
9 sights: iron sights, glow sights, reflex sight, combat scope (2.5x and 4x), short scope, medium scope, and night vision versions of the last two.
4 muzzles: none, bayonet, suppressor, and muzzle brake.
Custom reload animations (first person only) by Ha_ru [there's also alternative animations by chad509]
2 sets of custom sounds (recommended: Reverb and Ambiance Overhaul)

Textures are 2K and 1K (with 4K normal map for the main texture)

Stats:
Does more damage than the vanilla combat rifle, is a little more stable for full auto fire, but has less range, since the 8mm Kurz is a little heavy, being a shortened full rifle cartridge, and has a slightly slower rate of fire. It's a good weapon for what an assault rifle is designed for: general performance for up to medium range, good stopping power and controllable full auto, while being able to fire accurately in semi auto (it's not a sniper rifle though, hence the lack of long range scope).

It's quite a rare weapon, it can be found in the Museum of Witchcraft near the corpse of Major Jefferies, and is used by Captain Wes, the Gunner's commander, in Gunner Plaza (also improves his equipment, a bit out of the scope of the mod but since I was already editing him and making him more unique...). It has a rare chance to be found on epic loot and some vendors. It can sometimes be used by the railroad around level 30. It can also spawn as a legendary item.
If you want to use the console to spawn it, type "help sturm 4 weap" to get the ID.

It uses 5.56 rounds by default, but it's strongly encouraged to use the New Calibers version for the correct 7.92x33mm ammo.
It is compatible with See-Through Combat Scopes, including 2 combat scopes that can have the reticles customized if you have STCS or the STS Framework installed.

Compatibility:
It will be incompatible with other mods that change the same leveled lists. You'll need to make a merged patch in order to make it work with those mods. There are plenty of tutorials out there in fact. Link (by Skibadaa) As of version 1.1 it should be compatible with anything since it uses a script for the leveled lists.
For patches, see permissions section. I can consider making patches depending on what it is, so feel free to ask.

Installation: Use NMM or extract to the Data folder

Uninstallation: Make sure to unequip/drop/store the weapon and save your game. Then delete all files.

Changelog:
v1.0: Initial release
v1.01: Fixed FOMOD installer
v1.02: Fixed quiet firing sound
v1.03: Casings now eject on the correct side. Yay! Thanks to DOOMBASED for pointing out how to do it
v1.1:
-New attachments: reflex sight, muzzle brake (based on a real prototype STG muzzle device), folding/folded stock, short barrel, short magazine
-Improved textures, with 4K normal map
-New optional textures by The Edge (thanks!), selected ingame under Finish -> Worn
-Slight frequency variation for the firing sound so it sounds less dull/repetitive in full auto
-Minor balancing improvements
-Leveled List script
-For the New Calibers version, option of conversion to 5.56, 7.62x39 and .300 BLK
v1.2:
Custom reload animations
Improved firing sound
Custom NPC firing sound
New alternate set of sounds
Slower rate of fire

Known Issues:
Some clipping when using the short barrel with a bayonet. But putting a bayonet on a short weapon is a bad idea anyway :P
Some minor texture issues with back of the receiver when using the folding stocks.
Some smoothing issues.

Future plans:
None for now.

Credits:
Original model, worn textures: The Edge
Original textures: Megamawman
Handguard, ZF4 scope, and bolt: willbik
Suppressor: tigg
Bayonet: model by Sproily, textures by Millenia and Sam Fisher
Muzzle Brake: willbik and Sam Fisher
Folding stock: Raynox3D
7.92 Kurz model: KrazyGentleman
Sounds: Sam Fisher and willbik (alternate sound set by Partisan Executioner)
Reload animations: Ha_ru/blackxteel
Various model and texture edits: Sam Fisher
FO4 implementation: Sam Fisher
Leveled List script: Silant and DOOMBASED

Thanks to:
henkspamadres for See-Through Combat Scopes
willbik for his invaluable help
Ulfrsson for his advice
CanadianIcehole, PoisonedMods and H00V3RD8M for their help testing it

Tools used:
Blender
Maya
3ds Max
Quixel Suite
Photoshop
FO4Edit
Nifskope
Outfit Studio
Material Editor
Audacity
Creation Kit
FOMOD Creation Tool

My other mods:
Ducal Guard Service Revolver
M14 Standalone Rifle Retexture
M14 Standalone Rifle Resized Scopes
M9 Standalone Pistol New Grips