Open Math Notes

Resources and inspiration for math instruction and learning

Home Submit FAQ Contact My Notes

Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works in progress hosted by the American Mathematical Society as a service to researchers, teachers and students. These draft works include course notes, textbooks, and research expositions in progress. They have not been published elsewhere, and, as works in progress, are subject to significant revision. Visitors are encouraged to download and use these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto


PIerre Albin
University of Illinois, Urbana-Champaign
Reference #


Posted date
2017-01-18 18:34:54
Revised date
2017-01-18 18:52:08
Notes type
   Topics Course
      Geometric Analysis

Linear Analysis on Manifolds

This text is a version of the lecture notes used during a course at the University of Illinois at Urbana-Champaign in Spring 2012 and a course at the University of Rome ‘La Sapienza’ in Summer 2014, as well as several reading courses. Previous exposure to a course differentiable manifolds is assumed. The aim of the course is to introduce students to the techniques of geometric analysis on manifolds and establish the Atiyah-Singer index theorem.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v2 PDF (1.3M) 02/21/17