Is there a tool to backup my email inbox

I am running out of space at my current email provider and I hate being held hostage to upgrade my account.

I need to be able to backup my email regularly. This could be a scheduled job/cron etc. Preferably this should work on Linux. I would like to also run searches for my email on this tool. I am not expecting a cloud based services as I am more than happy with having it on my desktop (or my own servers). Is there any such tool?