Begriffsschrift is the name of a book on logic by Gottlob Frege published in 1879. The name Begriffsschrift is usually translated as concept writing or concept notation; the full title of the book identifies it as "a formula language, modelled on that of arithmetic, of pure thought."
Frege defines a logical calculus to support his research in the foundations of mathematics.
Begriffsschrift is both the name of the book and the calculus defined therein.
The calculus introduced quantifiers, and is essentially classical predicate logic, albeit in an idiosyncratic two-dimensional notation: connectives and quantifiers are written using lines connecting formulas, rather than the symbols ¬, and ∧, and ∀ in use today. For example, the implication between the B and A judgements, i.e. 
is designated with .
Nonetheless, some vestige of this notation survives: the symbol
that logicians informally call "turnstile" is derived from Frege's "Inhaltsstrich".
This little book is arguably the most significant publication in logic since Aristotle.
In the Tractatus Logico Philosophicus, Ludwig Wittgenstein pays homage to Frege in that he uses the term Begriffsschrift as a synonym for logical formalism.
A quote
„If the task of philosophy is to break the domination of words above human mind [...], then my concept notation, being developed for these purposes, can be a useful instrument for philosophers [...] I think, matter of logics has been forwarded just merely by the invention of this concept notation.”
(Frege: Begriffsschrift [Preface]).
References
- Gottlob Frege. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle 1879.
