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I had taken a first year geometry course over the summer in order to 'skip' it during the school year, and looking back it, I can say that it was one of the worst decisions I've made. Although I did well in the course and passed, one year later, I barely remember any of the material! I find geometry really interesting and want to thoroughly learn it; however, i do not know what level I should start at. The textbook used in the course was "Geometry" (McDougal Littell Jurgensen Geometry) and we went through most of the problems. I'm looking for a book that will re-strengthen my Euclidean geometry but also contain more advanced and interesting geometry topics. I plan to use the book for self-study, so it needs to be fairly understandable without a teacher at-hand. Here is a preliminary list that I have compiled:

Introduction to Geometry (AoPS): https://www.artofproblemsolving.com/store/item/intro-geometry

Geometry: Seeing, Doing, Understanding: https://www.amazon.com/Geometry-Seeing-Doing-Understanding-3rd/dp/0716743612

Euclidean and Non-Euclidean Geometries: Development and History:https://www.amazon.com/Euclidean-Non-Euclidean-Geometries-Development-History/dp/0716799480/ref=sr_1_1?s=books&ie=UTF8&qid=1466131637&sr=1-1&keywords=Euclidean+and+Non-Euclidean+Geometries%3A+Development+and+History

Fundamental Concepts of Geometry (Dover Books on Mathematics): https://www.amazon.com/Fundamental-Concepts-Geometry-Dover-Mathematics/dp/0486634159/ref=sr_1_1?s=books&ie=UTF8&qid=1466131731&sr=1-1&keywords=fundamental+concepts+of+geometry

Introduction to Geometry (Coxeter): https://www.amazon.com/Introduction-Geometry-H-S-Coxeter/dp/0471504580/ref=sr_1_1?s=books&ie=UTF8&qid=1466131885&sr=1-1&keywords=introduction+to+geometry+coxeter

Geometry Revisited: https://www.amazon.com/Geometry-Revisited-New-Mathematical-Library/dp/0883856190/ref=sr_1_2?s=books&ie=UTF8&qid=1466131885&sr=1-2&keywords=introduction+to+geometry+coxeter

Geometry (Brannan): https://www.amazon.com/Geometry-David-Brannan/dp/1107647835/ref=sr_1_1?s=books&ie=UTF8&qid=1466132022&sr=1-1&keywords=geometry+brannan

The Four Pillars of Geometry: https://www.amazon.com/Pillars-Geometry-Undergraduate-Texts-Mathematics/dp/0387255303/ref=sr_1_1?s=books&ie=UTF8&qid=1466132051&sr=1-1&keywords=four+pillars+of+geometry

This list is a very rough draft (it was practically built off of amazon reviews) so feel free to add any new items and/or remove any items you feel are inappropriate for my level (I have experience up to precalculus). I can only afford to purchase one textbook so an explanation of why you recommend/don't recommend a book would be appreciated.

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  • $\begingroup$ Coxeter's books are marvelous. Does not require calculus or higher algebra. I recommend them both. $\endgroup$ – DanielWainfleet Jun 17 '16 at 4:46

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