This course introduces homotopy type theory, which provides alternative foundations for mathematics based on deep connections between type theory, from logic and computer science, and
Such foundations are far closer to actual mathematics than the traditional ones based on set theory and logic, and are very well suited for use in computer-based proof systems, especially formal verification systems. We will use the Lean Theorem Prover in this course. Note that the latest version (Lean 3) doen not support Homotopy Type Theory (yet), so you must use Lean 2.
Basic topology and mathematical maturity will be assumed. Some familiarity with algebraic topology will be helpful, as will some familiarity with programming in a functional language. This course has a flavour very different from typical mathematics courses, so open-mindedness and willingness to learn alien concepts is essential.