"Kendini uzme"

This comes up as "Do not bring himself" but that makes no sense. Does it mean "Do not mention him/do not speak of him"?

 " Kendini üzme" = Do not upset yourself.

Kendin (yourself)+i     üz (root of the verb) + me (negatif )

the verb is Üzmek = to upset,to make s.o sad

Thank you   It all makes sense to me now.  How do I reply "It is hard not to be upset, but I will forget him now and get on with my life."

 You are wellcome. You can say like this.

"It is hard not to be upset, but I will forget him now and get on with my life."

" Üzülmemek zor ama Onu artık unutup kendi hayatıma (bakacağım) devam edeceğim"

When you put a word in brackets does this mean it is optional? Can I include it or exclude it without altering the meaning?

 Yes that means the word in brackets is alternative way to say..

 You can say in both ways..

" Üzülmemek zor ama Onu artık unutup kendi hayatıma devam edeceğim" OR

" Üzülmemek zor ama Onu artık unutup kendi hayatıma bakacağım.

Thank you once again tunci - I am grateful

 You are welcome Suadela.