The Pojective Geometry is a "Non Euclidean Geometry"?
When I say "Non Euclidean Geometry" I think Hiperbolic Geometry or Elliptic Geometry: Projective Geometry belongs to this set of geometry or not?

Thanks

Absolutely! Projective geometry in which any two lines intersect is non-Euclidean.

Hyperbolic and Elliptic geometries came from different interpretations of the Fifth Postulate and this is why the are commonly labeled non-Euclidean. Projective geometry was an independent development but is as much non-Euclidean as the other two.

In addition, any non-discrete geometry is also non-Euclidean. So geometries may be non-Euclidean but for different reasons.

Quite often the Taxicab geometry is presented as one of the variety. I believe it's a misnomer. In fact, I do not think it's a geometry at all. It's a metric space, yes, but not a geometry. It violates the most common requirement of having a single line through any two points.

Ok.
Projective Geometry, Hyperbolic Geometry and Elliptic Gemetry are non-Euclidean Geometry.

And Affine Geometry? Is Affine Geometry a non-Euclidean Geometry?

P.S.
I'm sorry for the quality of my questions, but I can't speak english very well.

Affine geometry is also non-Euclidean. E.g., in affine geometry the is no notion of angle measure. There are no right angles.

Euclidean geometry is based on five postulates and some common notions. There are a few axioms Euclid assumed implicitly without mentioning, e.g. that a straight line cuts the plane into two parts such that is a point from one is joint to a point on the other, the segment will cross the line. Or that two circles under certain conditions intersect in two points.

You should look whether a geometry violates any of the five postulates, although, as I said, I would not call "a geometry" a theory that allows more than one line through two points.

Ok.
Thanks very much.