Question: I have a bunch of music in iTunes on my old computer. How do I transfer my iTunes library to my new computer?

Answer: There are two ways to do this:
1) by manually copying your iTunes music files to an external hard drive and then manually copy them to your new computer.
2) using a program called iPod 2 iTunes that lets you copy music from your iPod directly to another computer.

I'll cover the manual route first, which is a little harder and requires that you have an external hard drive, and then I'll show you the easy way using just your existing iPod and an inexpensive copy of iPod 2 iTunes.

Manually copy your iTunes library to another computer using a external hard drive

Plug in your external hard drive to your computer. Open Windows Explorer and go to your iTunes music folder. On Vista it's C:\Users\your.username\Documents\My Music\iTunes\iTunes Music. On Windows XP it's under Documents and Settings.

Copy the iTunes Music folder to your external hard drive, and then plug the hard drive into the other computer.

Make sure iTunes is installed on the other computer, and just copy the contents of the iTunes Music folder from your external hard drive to the new computer (in the same location as the old computer). iTunes will recognize the files the next time you run it, and you'll be good to go.

Automatically copy your iTunes library to another computer using iPod 2 iTunes

A much easier option if you have all the music on your iPod is to use a program called iPod 2 iTunes, which will let you copy directly from your iPod to your computer.

Go into iTunes on your computer and make sure you've copied all of your music to your iPod. Then plug your iPod into the other computer and turn off iTunes when it starts.

Install and run iPod 2 iTunes, which will show you a list of all the music on your iPod. Just highlight all of the music files that you'd like to copy to the new computer, and click the Transfer button.

iPod 2 iTunes will automatically copy your iTunes library to your new computer.

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For more features about it, you can refer here.