Is there a way to back-up a my hotmail email account?
I have seen that I must install Windows Live Mail to do so, is there another way?
With any email POP3 client you can do that (Thunderbird, OutLook...). You have to configure it for your account, Here are the pop settings.
Incoming Server: pop3.live.com
Incoming Port: 995
SSL Encryption: yes
Outgoing Server: smtp.live.com
Outgoing port: 25 (use port 587 if the default port is not working)
TLS Or SSL: yes
If you have Outlook, you can configure it to connect to your Hotmail account and copy all the mail. Then you would have a local copy. Here are some instructions. Many other mail clients can perform the same task.
The easier way is to use Windows Live Mail application which works with Microsoft hotmail/live. Here is the link to download http://www.microsoft.com/download/en/details.aspx?id=36 Also you can use outlook with live connector free from Microsoft and have all emails available offline and can back them up using both the applications.