This document constitutes the theory and developer’s guide associated with the kernel of Code_Saturne. Combustion, electric and compressible modules are also presented. To make the documentation immediately suitable to the developers’ needs, it has been organized into sub-sections corresponding to the major steps of the algorithm and to some important subroutines of the code. In each sub-section (for each subroutine), the function of the piece of code considered is indicated. Then, a description of the discretisation follows. Finally, and more oriented towards the developers, details of the implementation are provided and a list of open problems is given (improvements, limitations...).