That depends entirely on what you mean by "close."
In most states, it is legal to marry a first cousin, so in that sense the state has descided that the relationship is not all that close. On the otherhand, first cousins who grow up close to each other are often considered almost part of the nuclear family.
One parent of you and one parent of the first cousin's are siblings
Your cousin's cousin is no relation to you.
Your mother's first cousin is your first cousin, once removed.
Your mother's first cousin is your first cousin once removed.
Your mother's first cousin is your first cousin, once removed
The child of your first cousin is your first cousin, once removed.
The wife of your first cousin is not related to you.
Your Aunt's first cousin may be your second cousin, onve removed or may be no relation to you at all.
Your Aunt's first cousin may be your second cousin, onve removed or may be no relation to you at all.
Cousin once removed.
Either your second cousin or your cousin in-law
Your daughter and your first cousin are first cousins, once removed.
Your grandfather's first cousin is your first cousin, twice removed. His second cousin is your second cousin, twice removed.