Some lectures notes:

• A master course on algebraic stacks (Toulouse 2005). cours1 cours2 cours3 cours4 cours4-2 cours5 cours6 cours7 cours8 cours9
• G-Theory of Deligne-Mumford stacks (Bologna 1999). PDF
• Lectures on non-abelian cohomology (MSRI 2002). PDF1 PDF2
• Homotopical algebraic geometry (Essen, 2002). PDF
• Homotopy types of algebraic varieties (Palo Alto 2004). PDF
• Tamsamani categories, Segal categories, and applications (IMA, 2004). PDF
• Hall algebras in the derived setting (Luminy 2006, notes taken by P. Nicolas). PDF

Videos:

• Lectures on non-abelian cohomology, MSRI, January 2002. Video
• Non-abelian Hodge structures, talk at IHES, March 2009. Video
• Symplectic and Poisson structures in the derived setting, talk at Cambridge April 2013. Video
• Deformation quantization and derived algebraic geometry, lectures series in Lisboa, June 2014. Video
• Deformation quantization and derived algebraic geometry, talk at IHES for M. Kontsevich’s 50th birthday. Video
• Deformation quantization and derived algebraic geometry, ICM-2014, Seoul. Video
• Quelques éléments de la pensée mathématique révolutionnaire d’Alexandre Grothendieck (lecture in french aimed at a very broad audience, Montpellier 2014). Video
• Problèmes de modules formels, Séminaire Bourbaki Janvier 2016. Vidéo
• Algebraic geometry, categories and trace formula, Clay Research Conference, September 2017. Video

Slides:

• Derived Geometry and Quantization, Colloque Solstice, Paris, Juin 2013. Slides
• Géométrie algébrique dérivée, Colloquium IMJ, Paris Mars 2014 .Slides
• Deformation quantization and derived algebraic geometry, ICM lecture. Slides
• A. Grothendieck et la poursuite des champs, Colloquium, Marseille 2015. Slides
• Motives and derived categories, Barcelona 2015. Slides
• Géométrie algébrique, catégories et formule des traces, Congrès de la SMF, Tours 2016. Slides
• Shifted Poisson Structures, Poisson 2016, Zurich, July 2016. Slides
• Algebraic Geometry, categories and trace formula, Clay Research Conference, Oxford 2017. Slides
• Catégories, formules des traces et géométrie algébrique, Colloquium Amiens, Janvier 2019. Slides

The videos of the DAGIT conference (June 2017).