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your uncle
That would be an uncle.
Your Grand Uncle(great uncle) would be your grandmother or grandfathers brother.
uncle
Your mother's mother is your grandmother.
that would be your grand uncle
Your Grand-mother's brother - would be your great-uncle
Grand Aunt or Grand Uncle depends what gender you are.
Your relation to your mums uncle is GREAT uncle. You're welcome! 
He is your uncle, in most families he would be Uncle (Jack, Fred or what ever his first name is).
A Great half uncle.
It would be your second cousin because your mothers uncle would be your great uncle his brother would still be your great uncle because he is still your mum's brother so then his daughter would your mum's niece and your cousin.