"This is Lord Henry, a good friend of mine"
What differences are there? It is just stylistic differences? Isn't?
Can I freely use such construction instead of "my/our etc"?
For example:
This is a house of ours .
I've met many friends of yours.
A teacher of mine said that…
And also such variant:
I've discovered much useful of yours.
Best Answer
In some situations, saying "my [x]" as opposed to "a [x] of mine" could imply that the subject of your sentence is one of a kind.
Example:
Because you have used the indefinite article this implies that you have more than one house, as if you had said "this is one of my houses", which would be more explicit.
If you said instead:
Although this does not exclude the possibility that you own more than house, it does not imply it either, and I think there would be an assumption you only own one. If you said "this is my home" that assumption would be even greater, as people tend to refer to just one place as their home, even if they own multiple properties.
With your example that refers to "a friend", I would say that, unlike houses, there is more of an assumption that most people have more than one friend. Therefore I would say there is no discernable difference between the statements "this is my friend" and "this is a friend of mine".
In the case of teachers which you mention in another example I would say that if it was to be assumed you only had one teacher at any given time, saying "my teacher" would imply uniqueness and perhaps that you are referring to your current teacher, whereas "a teacher of mine" implies either that you currently have, or have had more than one.
As in a lot of situations, context is everything and you should consider what your choice of words says about your specific subject.