Kock, Vainsencher: An invitation to Quantum Cohomology.
Written in the most friendly and motivating style I have ever seen in a book. Almost has no prerequisites: You should that there exists something like algebraic varieties - without having to know any technical details - and that P^1 is such a thing. Everything else is provided in easy exercises or the text. It gives an excellent intuition about the subject with lots of outlooks on a field of current research, and at the same time manages to be easily undergraduate readable.