To begin the archiving process go to: https://takeout.google.com/
Choose which of the Google services you'd like to archive.
You can choose as many as you like, but ensure you choose Mail.
Click Next Step when you have made your selections.
From here, click on Create Archive and you'll receive an email when it is finished.
You'll be able to download your archive from there.
Once Google is done archiving your emails you'll be able to download them.