Add music to iPhone after reinstalling computer

If you backed up your device, restore a copy

Restore your device from an iCloud or iTunes backup - Apple Support

Make sure you have authorized your iTunes account after the install

Authorize your computer in iTunes - Apple Support

Sgt.Connor wrote:

Hello. I'm having a problem adding music to my iPhone. I already synced it with my computer but after reinstalling Windows, iTunes requires me to erase the iPhone and sync everything from scratch. What should I do? I just need to add music to the library without downloading the whole list (306 songs) again.

Your question is not clear. Here is why:

"I just need to add music to the library ...". Which library:

• Your iTunes library on your computer? That would be done by simply downloading the 306 songs again.
• Your iPhone? That would be done by having the music in the iTunes library on your computer first, then syncing.