I am using Windows 8 with Windows Live Mail and would like to know who to make a backup - to an external disk - of my list of contacts e-mail addresses.

Inside the Windows Live Mail program, go into your Contacts section so you are looking at your address book. Then click Export on the toolbar here.
Also, if you login to the app using your Microsoft Account (in my screenshot, it's the toolbar icon on the far right with my picture on it). If you login there, your address book is always and automatically backed up for safe keeping, and you can view it anytime at people.live.com


The backup can be re-imported using the import button, which will then sort the contacts again alphabetically. The export itself isn't really designed to be "used" by itself.

Having said that, you can open it up inside a spreadsheet program like Excel, then sort them manually from the Excel sort button. But if you do this, I recommend making separate copy because editing the file in another program can render the backup unusable.