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?
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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.
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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.
It really depends on what kind of Geometry you want to get started in. Here my suggestions
Note: From now on, the books might not necessarily be introduction-books. This rather depends on your knowledge...
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.