This is a big question with a pretty easy answer. If you are like me you probably have thousands of emails in your inbox or other assorted folders. Since Evolution does not have a File--->Export function we will have to do it in a different way. The method is actually fairly simple.
Start Evolution
Select which folder you wish to export/backup. If you are like me you may have your mail in folders. For this exercise lets say you have a folder named "Fred's Junk".
Highlight "Fred's Junk" folder then you will need to select all. I am using Evolution 2.10.1 and there is no Select All in the Edit menu. No fear, use the keyboard shortcut CTRL-A. This will highlight all the messages in that Evolution folder.
Now that we have all the messages highlighted we need to save them. No problem
Go to File--->Save Message...
You should have a dialog window pop up asking where you want to save the message(s).
Select a folder in which you want to save messages and give the file a name. I suggest you give the file a name like Fred's Junk.mbx, the .mbx will denote to you that it is a mailbox.
Push the Save button and the messages will be saved in Fred's Junk.mbx. Depending on how many messages there are will determine how long the process is. I saved over 500 messages in my inbox so it took about 30 seconds to create the file.
Repeat the process for each folder in your Evolution inbox.
After you have all your email folders saved in this .mbx format they can easily be imported to other emial clients such as Thunderbird.
You may also want to know how to save your address book and filters. This is a fairly simple task as well. Your address book is stord in your home folder.
Adress book location
~/.evolution/addressbook/
I recommend saving the address book as an archive since there are lots of sub-folders. Open a file manager in the ~/.evolution folder. By default Nautilus does not show hidden files and folders. To show hidden files and folders open Naultilus and go to View--->Show Hidden FIles. Now that you can see hidden folders right mouse click on the addressbook folder and click Create Archive... Make sure you select .zip or .tar.gz as these archives will offer the best compatibility for all platforms (Windows/Linux/Mac).
Your filters are located in your /home folder in the follwing hidden folder.
~/.evolution/mail/filters.xml
I hope this procedure helps.
