Would you allow your boyfriend to read through your emails and go through your texts?

A few weeks ago, my boyfriend admitted to going through my emails and reading messages sent to me over a year ago, months before we even met. He got mad when he saw a suggestive message sent to me from a male friend. I was extremely upset that he violated my privacy, and I told him that I would not tolerate it in our relationship. Just yesterday, I caught him reading through my text messages while he thought I was sleeping. When I confronted him about it, he tried to deny it. I am so sick of this. What should I do?