How will i know if some other computer used my e-mail?

i only have the free software on my computer and i keep getting pop ups saying web page may not show. how or will i be able to tell if another computer has opened my email. is buying the software off the internet ok, if so which is better please help dumb dora over here! i think i changed my pword but it does not ask me for it is that because i am on my Computer