Building on Cantor's set theory and Frege's considerations on proof theory as well as Peano's symbolism, the Principia Mathematica successfully derived large areas of mathematics from a few basic logical concepts and axioms for the first time. To resolve the contradictions and paradoxes in logic and set theory, which led to a foundational crisis in mathematics, Whitehead and Russell developed the so-called type theory. In the introductions to their monumental work included in this volume, they present the paradoxes in logic and set theory and the type theory they developed, which has also inspired new models of thought and methods in the human sciences, such as those by Gregory Bateson, in a form accessible even to mathematically untrained readers.