Introduction to Homotopy Type Theory

This up-to-date introduction to type theory and homotopy type theory will be essential reading for advanced undergraduate and graduate students interested in the foundations and formalization of mathematics. The book begins with a thorough and self-contained introduction to dependent type theory. No prior knowledge of type theory is required. The second part gradually introduces the key concepts of homotopy type theory: equivalences, the fundamental theorem of identity types, truncation lev...