What Altshiller presents here is the cleanup of Roger Johnson's 1929 "Modern Geometry", which summarized the Euclidean geometry up to its time, was user unfriendly, quick-fixing in proofs and dumped most of the work onto the reader rather than giving the appropriate explanations.
Altshiller's book follows the concept of Johnson's. It is reviewed, and most of the mistakes are removed, if there were any. He brings exercises without solutions, type one which result d i r e c t l y out of the previous lesson and are actually fun to be worked out, and type two "supplementary exercises", often far beyond the theorems nearby and excessively difficult. This group should have been presented with hints and solutions - because, the way they stand now, some of them will never be solved.
Also, another modern edition would do some good, including a larger format and computerized (sketchpad) diagrams.
The difficult chapter on i n v e r s i o n with the new tricks You must learn
there runs too short in my opinion.
While the book is "intensively used", the paperback version falls apart.
In summary: a valuable addition on the small market of good geometry publications.