This book provides a definitive account of the theory, practice and applications of atom probe field ion microscopy (APFIM). The APFIM technique provides a unique method for observing and chemically identifying single atoms on solid surfaces. Recent advances in the method,which are largely due to the present authors, now permit the atomic-scale chemistry of a solid specimen to be recognised in three dimensions. As a result of these developments, new and exciting applications are rapidly emerging in the field of material science, surface science, and catalysis. The book is a state-of-the art account of this important field, and is intended for a graduate-level readership.