When does the first trimester end?

So I'm currently 12 weeks and 3 days and was a little confused because some things I read you aren't finished with the first trimester until after week 13 and some are at the end of 12. When does the first trimester actually end? And when will nausea go away? I was cooking and starving and the smell just made me super nauseous and not hungry anymore. So ready for second trimester!