This document is one of the course notes that I presented as part of the SIGGRAPH 2004 course called “The Elements of Nature: Interactive and Realistic Techniques.” They complement the paper that I published with Antoine McNamara, Adrien Treuille and Zoran Popovic on controlling fluids using the adjoint method at SIGGRAPH 2004. The paper presents a personal point of view. The paper also provides code to “adjoint” my simple fluid code that I presented at the Game Developer Conference in 2003.