A derived and homotopical view on field theories, Damien Calaque -- Part I Locality in Perturbative QFTs -- 2 Perturbative algebraic quantum field theory, Klaus Fredenhagen and Katarzyna Rejzner -- Lectures on mathematical aspects of (twisted) supersymmetric gauge theories, Kevin Costello and Claudia Scheimbauer -- 4 Snapshots of Conformal Field Theory, Katrin Wendland -- Part II Chern-Simons Theory -- Faddeev's quantum dilogarithm and state-integrals on shaped triangulations, Jørgen Ellegaard Andersen and Rinat Kashaev -- 6 A higher stacky perspective on Chern-Simons theory, Domenico Fiorenza, Hisham Sati and Urs Schreiber -- Factorization homology in 3-dimensional topology, Nikita Markarian & Hiro Lee Tanaka -- Manifoldic homology and Chern-Simons formalism (by Nikita Markarian) -- Factorization Homology and Link Invariants (by Hiro Lee Tanaka) -- Deligne-Beilinson cohomology in U(1) Chern-Simons theories, Frank Thuillier -- Part III (Semi-)Classical Field Theories -- Semiclassical quantization of classical field theories, Alberto S. Cattaneo, Pavel Mnev and Nicolai Reshetikhin -- Local BRST cohomology for AKSZ field theories: a global approach, Giuseppe Bonavolontà and Alexei Kotov -- Symplectic and Poisson geometry of the moduli spaces of at connections over quilted surfaces, David Li-Bland and Pavol Ševera -- Groupoids, Frobenius algebras and Poisson sigma models, Ivan Contreras -- Part IV Algebraic Aspects of Locality -- Notes on factorization algebras, factorization homology and applications, Grégory Ginot -- Index.