Is there an easy way to delete masses of emails in Gmail?

Alan's Gmail inbox needs tidying up, and it's easy to sort emails and save space using built-in search commands. But not before he makes a back up

Is there an easy way of doing mass deletes in Gmail? I've rather let the inbox grow, and I would like to trim it. Manual deletion would take forever. Yes, I know I should have archived important, useful emails. Slapped wrists! Alan

You may be surprised at how easy it is to delete thousands of Gmail messages with just a couple of clicks. The tricky bit is deleting the emails you don't want while keeping the ones you do. Computers are stupid and do what you tell them to do, which may not be what you intended. This is why you should take a backup before embarking on an email delete-fest, but I'll discuss that later.