Looking for an introductory textbook on algebraic geometry for an undergraduate lecture course I am now supposed to organize a tiny lecture course on algebraic geometry for undergraduate students who have an interest in this subject. 
I wonder whether there are some basic algebraic geometry texts considering the level of undergraduate students who have not learnt commutative algebra or homological algebra; they just know linear algebra and basic abstract algebra.
I am looking for some textbooks which provide a lot of examples (more computations using linear algebra and calculus). Actually, I am also looking for some textbooks based on very basic mathematics but which talk a little bit about a modern view point. 
Thanks in advance!
 A: The first volume of Kenji Ueno's "Algebraic Geometry" is a really nice undergraduate book.
A: Amnon Neeman's book does GAGA for projective space at the undergraduate level, or so he tells me.
[Edit: The book's called "Algebraic and Analytic Geometry".]
A: I recommend Harris' book. It has a nice pace, it is not very technical and has plenty of examples which can be worked out by simple linear algebra.
If your students have a good grasp in analysis you may also consider some parts from Griffiths-Harris, but that is probably too advanced.
A: I think Hulek's book is a nice introduction that does the commutative algebra as needed.  I think it is a little more demanding than some of the other suggestions though.
A: Introduction to Algebraic Curves by Phillip A. Griffiths
A: I suggest "Introduction to Algebraic Geometry" by Brendan Hassett.  It is a nice, down-to-earth introduction to algebraic geometry, and it also spends a lot of time on computational topics like Grobner bases.  When I was an undergraduate, I took a class from Brendan using an early version of this book (in fact, I think he was writing it as he taught), and it was completely accessible despite the fact that at time I did not know much commutative algebra.
A: You can also take a look at the question A learning roadmap for algebraic geometry.
A: An invitation to algebraic geometry by Karen Smith is excellent; it is very intuitive, and does everything over the complex numbers. For absolute newcomers, this is probably the best introduction.
Algebraic curves by William Fulton is a classic, quite easily readable for beginners, and free available online in pdf! (He recently published the third edition on his site.)
The books by Reid, Miranda and Hulek are also good. Reid does many explicit examples.
A: Miranda's "Algebraic Curves and Riemann Surfaces" assumes that you're familiar with a bit of complex analysis in one variable, but that's it.  One of my favorites, aside from the ones that everyone else posted.
A: I can't recall exactly how much background it assumes, but I found Reid's Undergraduate Algebraic Geometry quite accessible. (The forthright views in its last section can be taken either as a blemish or a bonus depending on one's POV.)
A: Cox Little and O'Shea's "Ideals varieties and algorithms" (http://www.amazon.com/Ideals-Varieties-Algorithms-Computational-Undergraduate/dp/0387356509/ref=sr_1_1?ie=UTF8&s=books&qid=1265456210&sr=1-1) is very accessible, assumes almost no background in commutative algebra, and has many examples. The emphasis is on computational algebraic geometry (including Groebner bases).  
BTW, Milne's "Algebraic Geometry" (http://jmilne.org/math/CourseNotes/AG.pdf) includes an "Annotated Bibliography" Appendix with an "Elementary Algebraic Geometry" section, and perhaps this is a good place to start the search.
A: I think Complex Algebraic Curves by Frances Clare Kirwan is a great introduction. In the first chapter,she speaks examples of brieskorn sphere. Abel's theorem is treated quite nicely. and much more!
