Complete error message : Arduino: 1.8.1 (Windows 10), Board: "Arduino Nano, ATmega328"C:\Program File - Pastebin.com
No idea why it is not working. This problem appears after I add the library for my MPU6050 gyroscope (And I'm pretty sure the library is not broken...)
It looks like you have the MPU6050 library files in your sketch folder, that's causing all those multiple definition errors. You should not have verbose output during compilation enabled in File > Preferences when you're posting errors to the forum unless you're having a build related issue or you're specifically requested to do so because it just clutters up the output with a lot of unnecessary stuff. You should always post the output in your forum post using code tags or if it's longer than the forum will allow then attach it to your post as a .txt file rather than on pastebin. This will make the information accessible to more people and thus give you a better chance of a solution. When you do post links use the chain links icon on the toolbar to make them clickable.
How else could I add it if not by adding it into the main directory?
Also, thank's for the advices. I appreciate.
Usually you will install a library to the libraries folder. This can be done automatically via Library Manager or Sketch > Include library > Add .ZIP library or you can manually install the library. That allows the library to be accessed from any sketch. The output you posted shows that indeed you do have the MPU6050 library installed in this way:
Using library MPU6050 in folder: C:\Users\Flabi\Documents\Arduino\libraries\MPU6050 (legacy)
It's also possible to put a library in the sketch folder. This is not as common but it can be useful if you want the sketch to be a self contained package or to use a specific version of the library.
From looking at the error messages it looks like the problem is the compiler is picking up both the library file installed normally and the library file included with your sketch, thus the multiple definition errors. If you have a good reason for leaving the library files in the sketch folder the solution might be as easy as changing the include syntax for the library from:
#include <MPU6050.h>
to:
#include "MPU6050.h"
but I can only guess since you haven't posted your code.