I'm following my first course in geometry and we're using the book "Geometry and Topology" by Miles Reid and Balázs Szendröi. Link
Now, the reason the book is chosen is because my professor believes it to be a great intuition builder. I however, care much more for formality than intuition and the proofs provided in the book are below the quality which is expected of us.
For the course, we'll only be delving in to chapters 1 through 5, but I would like a formal book on the subject. I've been looking at the questions previously asked, but I haven't been able to figure out which books would cover the same material.