The explosion energy of thermonuclear (Type Ia) supernovae is derived from the difference in nuclear binding energy liberated in the explosive fusion of light 'fuel' nuclei, predominantly carbon and oxygen, into more tightly bound nuclear 'ash' dominated by iron and silicon group elements. The very same explosive thermonuclear fusion event is also one of the major processes contributing to the nucleosynthesis of the heavy elements, in particular the iron-group elements. For example, most of the iron and manganese in the sun and its planetary system were produced in thermonuclear supernovae. Here, we review the physics of explosive thermonuclear burning in carbon-oxygen white dwarf material and the methodologies utilized in calculating predicted nucleosynthesis from hydrodynamic explosion models. While the dominant explosion scenario remains unclear, many aspects of the nuclear combustion and nucleosynthesis are common to all models and must occur in some form in order to produce the observed yields. We summarize the predicted nucleosynthetic yields for existing explosion models, placing particular emphasis on characteristic differences in the nucleosynthetic signatures of the different suggested scenarios leading to Type Ia supernovae. Following this, we discuss how these signatures compare with observations of several individual supernovae, remnants, and the composition of material in our galaxy and galaxy clusters.

Author version of a chapter for the 'Handbook of Supernovae', edited by A. Alsabti and P. Murdin, Springer. 22 pages, 2 figures