This is a graduatelevel guide to loop quantum
gravity. I hope this will help the reader find
the "prerequisites" as well as some of the more contemporary work on
this approach to quantum gravity. Suggestions are welcome.
You're encouraged not to read linearly (this is, afterall, a
nonlinear field!) For instance, you might start with the more recent
book, "Quantum Gravity" by Carlo Rovelli, which covers most of these
topics, or the older book of Abhay's
("Lectures..."  the little blue book), or the shorter, more
inspirational, reviews and primers and then
backtrack to pick up the background you find you need.
Be aware that the field has evolved greatly since the mid1990's! I have retained older works, since they occasionally come in handy. I will (hopefully soon) include sections on the areas of spin foams and loop quantum cosmology.
Enjoy!
 Seth Major (based on an earlier reading list by Troy Schilling and
myself)
Constrained Systems:
 P.A.M. Dirac, Lectures on Quantum
Mechanics, (Yeshiva, New York, 1964) [QC174.1.D55].
 M. Henneaux and C. Teitelboim, Quantization of
Gauge Systems, at least Chapters 1, 2, 4, and 13 (on quantization) (Princeton, 1992). [QC793.3.F5H46
1992].
 Joe Romano, ``Geometrodynamics vs. Connection
Dynamics'' in General Relativity and Gravitation, 25
(1993) 759 (This is Joe's Ph.D. thesis, Syracuse 1991).
 Abhay Ashtekar, Lectures on NonPerturbative
Canonical Gravity, Appendix B, (World Scientific, Singapore, 1991)
[QC178.A48 1991].
Hamiltonian Formulation of GR  3+1:
 R. Wald, General Relativity, Apendix E,
(Chicago, 1984) [It's all in the book but you have to hop back and forth
from chaper to appendix].
 Thomas Thiemann, Modern Canonical Quantum Gravity (Cambridge Univeristy Press, 2007) ISBN 0521842638.
 A. Ashtekar, New Perspectves in Canonical
Gravity , pg. 37, (Bibliopolis, Napoli, 1988) [QC178.A73 1988].
Connection Variables:
 Abhay Ashtekar and Jerzy Lewandowski Background Independent Quantum Gravity: A Status Report grqc/0404018.
 Carlo Rovelli, Quantum Gravity (Cambridge Univeristy Press, 2004) ISBN: 0521837332.
 Thomas Thiemann, Modern Canonical Quantum Gravity (Cambridge Univeristy Press, 2007) ISBN 0521842638.
 Joe Romano, ``Geometrodynamics vs. Connection
Dynamics'' in General Relativity and Gravitation, 25
(1993) 759 (This is Joe's Ph.D. thesis, Syracuse 1991).
 A. Ashtekar, Mathematical problems of
nonperturbative quantum general relativity in Les Houches 1992, [B.
Julia ed., Les Houches 1992 (1994)].
 Abhay Ashtekar, Lectures on NonPerturbative
Canonical Gravity, (World Scientific, Singapore, 1991) [QC178.A48
1991].
Quantization:
 Abhay Ashtekar and Jerzy Lewandowski Background Independent Quantum Gravity: A Status Report grqc/0404018.
 Thomas Thiemann, Lectures on Loop Quantum Gravity grqc/0210094.
 Carlo Rovelli, Quantum Gravity (Cambridge Univeristy Press, 2004) ISBN: 0521837332.
 Thomas Thiemann, Modern Canonical Quantum Gravity (Cambridge Univeristy Press, 2007) ISBN 0521842638.
 J. Pullin Knot Theory and Quantum Gravity in
Loop Space: A Primer , hepth/9301028 (breezy but still inspiring!).
 Carlo Rovelli and Peush Upadhya Loop quantum
gravity and quanta of space: a primer grqc/9806079 (updated but even
more brief).
 Rodolfo Gambini and Jorge Pullin Loops, Knots,
Gauge Theories and Quantum Gravity (Cambridge University Press 1996
ISBN 0521473322)
 John Baez Gauge Fields, Knots and Gravity
(World Scientific 1994 ISBN 9810220340 (paperback))[QC793.3.F5 B33 1994]
 Volume 434 of SpringerVerlag's Lecture Notes in
Physics, Canonical Gravity From Classical to Quantum is the
proceedings of a conference held in September 1993.
 R. Geroch, Geometrical Quantum Mechanics,
pdf and a
link to Rob Salgado's site with the LaTex source.
 Abhay Ashtekar, Lectures on NonPerturbative
Canonical Gravity, Ch. 10, (World Scientific, Singapore, 1991)
[QC178.A48 1991].
Classical Mechanics  Symplectic
structures:
 V.I. Arnold, Mathematical Methods of Classical
Mechanics 2nd ed., pg. 201 (SpringerVerlag, New York, 1989)
[QA805.A6813 1989].
 A. Ashtekar, Lectures on NonPerturbative
Canonical Gravity, Appendix B, (World Scientific, Singapore, 1991)
[QC178.A48 1991].
Fibre Bundles:
 C. Nash and S. Sen, Topology and Geometry for
Physicists , pg. 140, (Academic, London, 1983) [QA611.N35].
 C. Isham, Modern Differential Geometry for
Physicists, pg. 111 (World Scientific, 1989).
 M. Nakahara, Geometry, Topology and
Physics, Ch. 9, (Adam Hilger, 1990) [QA641.N35 1990].
 A. Ashtekar, G. Horowitz, and A. MagnonAshtekar,
General Relativity and Gravitation, 14 (1982) 411.
 Y. ChoquetBruhat and C DeWittMorette,
Analysis, Manifolds and Physics, Amsterdam; N.Y., NorthHolland
Pub. (1981) [QC20.7.A5C48 1981].
Connections in Field Theory/on Principal Bundles:
 Your favorite field theory book or L.D. Faddeev and
A.A. Slavnov, Gauge Fields: Introduction to Quantum Theory, Ch 1
and 3 (an old style for field theory but closer to the language used around
here) (Benjamin/Cummings, Reading, MA, 1980), [QC793.3.F5S5213].
 L. Kauffman, Knots and Physics, pg. 293
(just after the little bit on SU(2)) (World Scientific, Singapore, 1991)
[QC20.7.K56K38 1991] .
 Jackiw in Les Houches, Relativity, B. DeWitt and R.
Stora, eds. [QC174.13.R45 1984].
 M. Nakahara, Geometry, Topology and
Physics, Ch. 10, (Adam Hilger, 1990) [QA641.N35 1990].
Tetrads:
 S. Weinberg, Gravitation and Cosmology, pg.
385 (Wiley, New York, 1972).
 R. Wald, General Relativity, pg. 49,
(Chicago, 1984).
Spinors:
 W. Bede and H. Jehle, Rev. Mod. Phys.
25 (1953) 714 (old and from the point of view of the Dirac
equation).
 L. Kauffman, Knots and Physics, pg. 392
(esp. 398).
 R. Penose and W. Rindler, Spinors and
Spacetime Volume 1, (Cambridge, 1984) [QC20.7.S65P46 1984].
 A. Trautmann, F. Pirani, and H. Bondi, Lectures
on General Relativity, Ch. 3, (PrenticeHall, 1965) [QC6.B675 1964].
 G. Sterman, An Introduction to Quantum Field
Theory, pg. 119, (Cambridge, 1993).
 A. Ashtekar, Lectures on NonPerturbative
Canonical Gravity, Appendix A, (World Scientific, Singapore, 1991)
[QC178.A48 1991].
Spin Networks:
 Seth Major, ``A spin network primer'' Am. J.
Phys. 67 (1999) 972980 grqc/9905020.
 Roberto De Pietri and Carl Rovelli ``Geometry
eigenvalues and the scalar product from recoupling theory in loop quantum
gravity'' Phys. Rev. D 54 (1996) 26642690.
Loops (for historical interest):
 Jorge Pullin Knot Theory and Quantum Gravity in
Loop Space: A Primer , hepth/9301028 (breezy but inspiring!).
 For a broad review try C. Rovelli in Living Reviews or Class. and
Quantum Grav. 8 (1991) 1613 or L. Smolin in Proceedings of
the XXII Gift International Seminar (World Scientific 1992). Or, read
the orginal paper: C. Rovelli and L. Smolin. Nuc.Phys. B331
(1990) 80.
 Carlo Rovelli Quantum Gravity (Cambridge University Press 2004) ISBN: 0521837332
 B. Brügmann, On the constraints of quantum
general relativity in the loop representation, Ph.D. thesis, Syracuse
University (May 1993).
 B. Brügmann, Loop Reprentations ,
grqc/9312001.
 Thomas Thiemann, Modern Canonical Quantum Gravity (Cambridge Univeristy Press, 2007) ISBN 0521842638..
 Abhay Ashtekar, Lectures on NonPerturbative
Canonical Gravity, Ch. 15 and 16, (World Scientific, Singapore, 1991)
[QC178.A48 1991].
