David Hilbert was particularly interested in the foundations of mathematics. Among many other things, he is famous for his attempt to axiomatize mathematics. This text is his treatment of symbolic logic which lays the groundwork for his later work with Bernays. This translation is based on the second German edition, and has been modified according to the criticisms of Church and Quine. In particular, the authors' original formulation of Godel's completeness proof for the predicate calculus has been updated."