We deal with germs at the origin of reversible mappings in R-3. Normal forms and generic deformations (of fired points) of such diffeomorphisms are presented. We perform this by applying tools of the Singularity Contact Theory between surfaces together with analytical invariants of the trace function. The normal forms are found via Computer Algebra algorithms. We also define a notion of a codimension for these singularities, exhibit their generic deformations, and present some bifurcation diagrams. AMS (MOS) subject classification: 58F36, 58F14, 14-04.716596