Starting point for learning etale cohomology

Question

I am currently interested in learning etale cohomology. My background is what you could find in Hartshorne (mostly in chapter II and III) and I also have strong intuition from algebraic topology. I heard that there are several good references on this topic

• Kiehl, Etale Cohomology and The Weil Conjectures.
• Lei fu, Etale Cohomology Theory.
• Milne, Lectures on Etale Cohomology.
• Tamme, Introduction to Etale Cohomology.

I incline to use Leifu's book, but I wonder whether the author treats too many auxiliary results so I desire a roadmap for reading this book. Also, I appreciate any comment about the pros and cons of each of the aforementioned books. Thanks in advance.

Answer 1

Question: "Also, I appreciate any comment about the pros and cons of each of the aforementioned books. Thanks in advance."

Answer: I want to recommend Milnes "Etale cohomology" from 1980 - a self contained book. You need to know some commutative algebra ala Atiyah-Macdonald or Matsumuras book. The book "gives all details" and I believe it is better than the "Lectures on etale cohomology"-book.