Introduction to Geometry Books I am looking for a book that covers introduction to geometry. Currently, I am reading "Geometry: A metric approach with models", by R.S Millman. I like the book but I would like to read another highly recommended book(s) to go along with it.
Are there any other highly recommend book which will be good for an introduction to geometry that will ideally have a solution manual?
 A: It really depends on what kind of Geometry you want to get started in. Here my suggestions

General Geometry



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*Geometry for Dummies - very basic

*The Elements - Euclid

*Geometry Unbound - Kedlaya - very good (and free)

*Essential Geometry: A Self-Teaching Guide - Tim Hill

*Plane and Solid Geometry - Aarts



Olympiad Geometry



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*Euclidean Geometry in Mathematical Olympiads - Evan Chen - Excellent

*Introduction to Geometry - Richard Rusczyk 

*Problem-Solving and Selected Topics in Euclidean Geometry - Louridas


Note: From now on, the books might not necessarily be introduction-books. This rather depends on your knowledge...

Analytic Geometry



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*An Introduction to Analytic Geometry and Calculus - A.C. Burdette



Non-euclidean Geometry



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*Introduction to Non-Euclidean Geometry - Harold E. Wolfe



Algebraic Geometry



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*Geometry of algebraic curves - Arbarello



Differential Geometry



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*An Introduction to Differentiable Geometry - T. J. Willmore

*Differential geometry: manifolds, curves, and surfaces - Berger

*Curves and surfaces - Abate



Discrete Geometry



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*Lectures on Discrete Geometry - Matousek



4d-Geometry



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*Beyond the Third Dimension - Thomas F. Banchoff

*If you prefer videos, here you can find awesome explanations for the different dimensions



Addendum
I've just remembered, that there's a really nice book on geometry I would like to recommend you: Episodes in nineteenth and twentieth century Euclidean Geometry (from Ross Honsberger).
This book might not offer an introduction to geometry - however, it presents very interesting geometry properties (especially in triangles - the most studied geometry polygon) that can be proven with clever manipulations of elementary geometry.
A: If you are looking for a very detailed treatment of Euclidean geometry with rigorous proofs from axioms, I'd recommend John Lee's Axiomatic Geometry.  No solution manual, although many theorems proved in detail in the text serve as good examples for the exercises.
A: I personally enjoyed "Elementary Geometry from an Advanced Standpoint," by Edwin Moise. It has some nice historical remarks on how early ideas about ratios were essentially closely related to Dedekind cuts, etc. And Coxeter's books are pretty widely admired, although I've only dipped into them here and there. 
