What are absolute geometries?

Question

Mathematics

There is such a term: absolute geometry. This is a geometry that satisfies the axioms of Euclid except for the axiom of parallelism, or its analogues.
Interested in the following questions:

1. Is it true that absolute geometry is either the geometry of Lobachevsky or the geometry of Euclid. If so, where can I read the proof?
   
2. How is the axiom "A circle can be described from any center by any radius" interpreted in absolute geometry?
   
3. Do you know a detailed reading on this topic?
   

The second question is related to the fact that on the page "Absolute Geometry" on Wikipedia it is indicated that there is no metric in absolute geometry, and therefore it is not clear how to define a circle.

Answer 1

Such a perversion is also possible: in one place there will be Lobachevsky properties (a bunch of lines parallel to the given one can be drawn through a point), in another - Euclid (exactly one).
The concept of "distance" - |AB| - there is. There is no concept of "movement", and therefore it is possible to draw a circle, but to draw a circle equal to it, so that it has similar properties, for example, the same area - no.