Modern Geometry book to match my course description

[MidgetDwarf]

MATH 4300 - Modern Geometry
(3)
Prerequisite: MATH 3450 with minimum C grade. Topics selected from advanced Euclidean geometry, non-Euclidean geometry, projective geometry. May be repeated once for credit with approval of instructor as subject matter changes.

The above paragraph is the course description for a course I am interested in taking. Can anyone recommend me a book to study over the summer? The teacher does not use any official course book.

How difficult is this course? Things I should know before my first day? Math3450 is a proof course.

 

[The Bill]

I like the textbook Modern Geometries by Michael Henle. I have the 1996 1st edition. There is a more expensive 2001 2nd edition, but I think the 1st edition is fine for covering introductory non-Euclidean geometry.

 

[mathwonk]

I think the best recent geometry book is Geometry: Euclid and beyond, by Robin Hartshorne, with a copy of Euclid at hand for reference, such as the green lion press version.

https://www.amazon.com/dp/1888009195/?tag=pfamazon01-20

 

[MidgetDwarf]

Thanks for the rec. I do have the Green Lion edition of Euclid (hardcopy). My school has a copy of Hartshorn book. Maybe I should go through Euclid. I have been putting it off for 2 years.

@ I think I read somewhere that you do algebraic geometry. The field of Geometry has always fascinated me. If I wanted to say, learn algebraic geometry, or even become an algebraic geometer. What are some of the core classes or books, I should tackle as an undergrad?

 

[mathwonk]

maybe miles reid's books, undergraduate commutative algebra and undergraduate algebraic geometry, then maybe william fulton's book on algebraic curves (free on his website)?

http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf

but algebraic geometry can also use algebraic topology and complex analysis, both one and several variables, as well as homological algebra.

another excellent undergraduate/graduate book is rimenna surfaces and algebraic curves by Rick Miranda, and algebraic curves by robert walker, but that is more old fashioned.