The following are PDF files of scanned hand-written notes. The author intends to compile them into an introductory string theory textbook for a mathematical audience, covering the massless spectrum of the five standard string theories and related topics.

These notes are from a series of lectures given at Microsoft Research from August 1999 through March 2000 while the author was a Post Doctoral Researcher in the Theory Group.

• Lecture 1
  Introduction, loops on R, bosonic Fock space, Virasoro algebra.
• Lecture 2
  Reparameterization invariance, Lie algebra and BRST cohomology, 26 dimensional bosonic string.
• Lecture 3
  Second quantization, left- and right-movers, massless closed string spectrum, tachyons and gravitons.
• Lecture 4
  Tensor fields and conformal weight, Fermionic strings, Ramond and Neveu-Schwarz sectors.
• Lecture 5
  Virasoro central charge, bosonization, partition functions, operator-valued functions.
• Lecture 6
  Vertex operators, Operator Product Expansion (OPE), Wick's Theorem.
• Review
  Recapitulations of earlier results in terms of vertex operators.
• Lecture 7
  Supersymmetry, superspace, super Virasoro algebra, supersymmetric BRST construction, 10 dimensional superstring.
• Lecture 8
  Superstring spectrum, representations of SO(8), supersymmetric multiplets, GSO projection.
• Lecture 9
  Type IIA/B string, Heterotic string, SO(32) and E8xE8, Loop groups and even unimodular lattices.
• Mirror Symmetry
  T duality, N=2 superconformal algebra, chiral primary fields, cohomology, spectral flow.
• The super Poincare algebra
• Strings & Topology
  A colloquium-style talk showing how cohomology appears in N=2 supersymmetry, and using superstrings to compute the orbifold Euler characteristic and cohomology of a K3 surface.
• Torus Moduli
• K3 Moduli

• Introduction to Strings
  An undergraduate talk given at Reed College, describing the physics leading up to string theory.
• String Theory for Algebraists (slides)
  The usual technical introductory string theory spiel, tweaked for algebraists rather than physicsts.

• Paul S. Aspinwall, K3 surfaces and string duality, in Surveys in Differential Geometry 5, IP, 1999.
• Pierre Deligne et al. (eds.), Quantum Field Theory and Strings: A Course for Mathematicians, Vols. 1 & 2, AMS/IAS, 1999.
• Daniel S. Freed, Five Lectures on Supersymmetry, AMS, 1999.
• M. B. Green, J. H. Schwarz & E. Witten, Superstring Theory, Volumes I & II, Cambridge, 1987.
• Victor Kac, Vertex Algebras for Beginners, Second Edition, ULS 10, AMS, 1998.
• Joseph Polchinski, String Theory, Volumes I & II, Cambridge, 1998.
• Cumrun Vafa, lecture notes from a string theory course at Harvard, Fall 1994.