Part III Lecture Notes on Operators on Hilbert Space - Michaelmas 1991, Cambridge: ps

Part III Lecture Notes on the Atiyah-Singer Index Theorem - Michaelmas 1996, Cambridge: ps

Part III Lecture Notes on Kac-Moody and Virasoro Algebras - Michaelmas 1998, Cambridge: ps

Part IB/II Lecture Notes on Functional Analysis - Lent 1999, Cambridge, lectures 1-16 : ps, lectures 17-24: ps 

Part II Lecture Notes on Hilbert Spaces - Lent 1996, Cambridge: ps, Graham Allan's adaptation (2002): ps

Part II Lecture Notes on Partial Differential Equations, Cambridge: ps, Mark Joshi's adaptation: ps
 
Part III Lecture Notes on Analysis of Operators - Michaelmas 2006, Cambridge, provisional version without appendices: ps
(previously MSRI 2000, ENS Paris 2002, CIRM 2004, Chateau Gombert 2006)

Minicourse on Bott Periodicity and Index Theorems -  Isaac Newton Institute, Cambridge, 2006: ps
(also Marseille 2007)

Part III Lecture Notes on von Neumann Algebras - Lent 2008, Cambridge, without supplementary material: Part I Part II
(also Marseille IML 2007, LATP 2007)