I would like some reference regarding geometry. I'm a student of civil engineering, and I wanted some insight in general geometry, e.g, know what originated it, what is valid today, etc. In specific, a book with rigorous explanations of analytic geometry would help a lot. Resuming: I want a book that "situates" me in time, and that explains generals terms of geometry and their respective development. Of course, I know some things, but a general overview would be better, can't afford mediocrity.
I want to ask also what is the most valid geometry used today. I know we have non-Euclidean geometries, but what is the most suitable for working in engineering? Euclidean it's fine? It's recomendable to read it directly from the "Elements"?
It's hard to limit the selection to one book. One that I have always enjoyed is " Geometry and the Imagination " by David Hilbert and S. Cohn-Vossen . But I'll write down a few authors that come to mind. " Introduction to Geometry" by H.S.M. Coxeter, a great Geometer and expositer . Perhaps also "Euclidean and Non-Euclidean Geometries: Development and History" by Marvin J. Greenberg .
That said, there are a number of excellent Geometry books available at archive.org, hundreds in fact and many of them are excellent. There is also something of a rating system to allow you to judge by the number of downloads which books are great. I'd actually check there first! I found my college Differential Geometry book, " Elementary Differential Geometry" by Barrett O'Neill there. Quite a find.
I haven't mentioned Analytic Geometry - something you might actually use on a regular basis, but I would consider searching archive.org just for a start.