"check out", "check in", or just "check"?

Question

what is the grammatically right way to say I enquire is some new letters come into my e-mail post-box. I mean is one of the following correct:

1. I check my e-mail
2. I check out my e-mail
3. I check in my email.

Answer 1

To "check" something is to examine it. So the first is correct.

To "check in" something is to register it. So the third is not correct.

To "check out" could mean either "register" (for taking out, e.g. a library book), OR to examine. So the second is ok, but the first is more common.

Answer 2

For the three statements you give, the first is correct. You could use the second "I check out my email", which is perhaps a more colloquial approach, but the first option is by far the most widely used and understood. The third is incorrect.