I need some good reference for studying valuations, I was looking for some really detailed material, as I'm just starting to study this theme. Please help.
Chapters 5,9 and 10 of Atiyah--Macdonald are a good algebraic reference http://www.math.toronto.edu/jcarlson/A--M.pdf
But as a number theorist I prefer Chapter II of Neukirch https://www.cimat.mx/~luis/seminarios/Teoria-de-Numeros/Neukirch_Algebraic_number_theory.pdf
Most books on Commutative Algebra should cover the basics, for example "Introduction to Commutative Algebra" by Atiyah and MacDonald, or "Commutative Ring theory" by Matsumura (not to be confused with his older book "Commutative Algebra").