This package provides methods to "add" two R tables; also an alternative interpretation of named vectors as generalized R tables, so that c(a=1,b=2,c=3) + c(b=3,a=-1) will return c(b=5,c=3). Uses disordR discipline (Hankin, 2022, <doi:10.48550/arXiv.2210.03856>). Extraction and replacement methods are provided. The underlying mathematical structure is the Free Abelian group, hence the name. To cite in publications please use Hankin (2023) <doi:10.48550/arXiv.2307.13184>.