The game crashes due to missing dependencie. Even though I added it to the build.gradle file and to the fabric.mod.json file.

Here is the log:

[15:53:24] [main/INFO]: Loading for game Minecraft 1.14.4
Exception in thread "main" java.lang.RuntimeException: Failed to resolve mods!
	at net.fabricmc.loader.FabricLoader.load(FabricLoader.java:147)
	at net.fabricmc.loader.launch.knot.Knot.init(Knot.java:120)
	at net.fabricmc.loader.launch.knot.KnotClient.main(KnotClient.java:26)
Caused by: net.fabricmc.loader.discovery.ModResolutionException: Errors were found!
 - Mod gui_test_mod depends on mod {libgui @ [1.3.0]}, which is missing!
	at net.fabricmc.loader.discovery.ModResolver.findCompatibleSet(ModResolver.java:324)
	at net.fabricmc.loader.discovery.ModResolver.resolve(ModResolver.java:504)
	at net.fabricmc.loader.FabricLoader.load(FabricLoader.java:145)
	... 2 more

I've ran genSources multiple times to see if that is the problem but even so that doesn't affect the result.

Here's the depends section in the fabric.mod.json file:

"depends": {
    "fabricloader": ">=0.4.0",
    "fabric": "*",
    "libgui":"1.3.0"
}

And here's the dependencies section of the build.gradle file:

dependencies {
	minecraft "com.mojang:minecraft:${project.minecraft_version}"
	mappings "net.fabricmc:yarn:${project.yarn_mappings}"
	modCompile "net.fabricmc:fabric-loader:${project.loader_version}"

	// Fabric API
	modCompile "net.fabricmc.fabric-api:fabric-api:${project.fabric_version}"

	// LibGui
	modCompile "io.github.cottonmc:LibGui:1.3.0"
}

I'm also very new to fabric, but honestly I feel like these sort of things should come across pretty straight forward if you look at the documentation. At least I can say that LibGui's documentation is pretty damn bad.

I don't think that this is an issue, it might as well be an issue but on the LibGui side of things. Or, kind of most likely, a mistake by me.

Anyway, thanks for any HELP!

Well now the Cotton Team's website is not available.

For what it's worth, the actual libgui documentation is available on Cotton Team's website rather than on the actual repository. Apart from that, this does not look like the issue has anything to do with Fabric API, which this issues tracker is for.