Foster was an expert in Latin literature, especially Cicero, and was an internationally recognized authority on the Latin language. He taught Latin as a living language and influenced many Latinists; Nancy Llewellyn was inspired by Foster to found Septentrionale Americanum Latinitatis Vivae Institutum (SALVI), the North American Institute of Living Latin Studies, in 1997, and two former students, Jason Pedicone and Eric Hewett, in 2010 revived his summer school in Rome as Living Latin in Rome, a program for college students, and have founded a non-profit organization, the Paideia Institute, which now also sponsors courses in other countries and in Greek, as well as elementary-school programs in the US. Foster headed the effort to produce a modern Latin dictionary, "Lexicon Recentis Latinitatis", published in 1992–1997. After retiring, he published "The Mere Bones of Latin (Ossa Latinitatis Sola)" with the Catholic University of America Press in 2016; a second volume is forthcoming.