Frege was the father of modern mathematical logic. In 1879 he published Concept-notation, a work that included a formal language which was able to express generality through the quantifier-variable notation. This work also set forth a version of second order quantificational logic whcih he used to develop a logical definition for the ancestral of a relation. He was incredibly influential on the later works of Wittgenstein, Russell, George Boole, and Ernst Schroeder.
In "On Sense and Meaning" Frege grapples with the problems of the difference between meaning and reference, and between proper name and its sense. He opened up new areas in the study of sense and meaning that were widely written on for the next 5 decades.