Grammatology is the study of writing. Of writing in a narrow sense — abc..., αβγ... etc. —, but also of writing as a medium and as the symbol of knowledge.
Ignace J. Gelb coined the term in 1952 in his Study of Writing as a designation for a new discipline with the objective "to establish general principles governing the use and evolution of writing on a comparative-typological basis" (Gelb, Ignace Jay. A Study of Writing. Revised Edition, Chicago: University of Chicago Press, 1974, S. v).
Jacques Derrida used the same term in his 1967 De la grammatology and extended it to a fundamental critique of Western thought. Since then these two points of view have coexisted.