How do I transfer my music from the ipod nano to my apple mediathek? Lost all music on my PC after system breakdown.

What is "apple mediathek"?

Based on context, I'll assume you are asking how to off-load song files from an iPod to a computer. iTunes syncing is generally in one direction only, from iTunes library to iPod. You cannot use iTunes to transfer song files from iPod to computer (except for songs purchased from the iTunes Store)

NOTE: Songs purchased from the iTunes Store can be downloaded again at no cost, from the iTunes Store Purchased screen.

Download your past purchases - Apple Support

However, there are third-party methods and utilities that can transfer from iPod to computer. If you do an Internet search on something like "ipod music transfer," you should get some links (including an article by CNET on the topic). Once the iPod's song files are on your computer's drive, add them to your current iTunes library.

Going forward, you should back up your iTunes data. This Apple document describes one way to back up your complete iTunes folder to an external drive.

Manage and back up your iTunes media library - Apple Support

This method should also be used when switching from an old computer to a new computer. By transferring or restoring your complete iTunes folder, it's the same iTunes library on the new computer, not a new iTunes library with your old songs. iPods are not designed to be your iTunes data backup.