The Fourth International Conference on Automatic Di?erentiation was held July20-23inChicago,Illinois.Theconferenceincludedaonedayshortcourse, 42 presentations, and a workshop for tool developers. This gathering of au- matic di?erentiation researchers extended a sequence that began in Breck- ridge, Colorado, in 1991 and continued in Santa Fe, New Mexico, in 1996 and Nice, France, in 2000. We invited conference participants and the general - tomatic di?erentiation community to submit papers to this special collection. The28acceptedpapersre?ectthestateoftheartinautomaticdi?erentiation. The number of automatic di?erentiation tools based on compiler techn- ogy continues to expand. The papers in this volume discuss the implem- tation and application of several compiler-based tools for Fortran, including the venerable ADIFOR, an extended NAGWare compiler, TAF, and TAPE- NADE. While great progress has been made toward robust, compiler-based tools for C/C++, most notably in the form of the ADIC and TAC++ tools, for now operator-overloading tools such as ADOL-C remain the undisputed champions for reverse-mode automatic di?erentiation of C++. Tools for - tomatic di?erentiation of high level languages, including COSY and ADiMat, continue to grow in importance as the productivity gains o? ered by high-level programming are recognized.