### Annotated Bibliography

- Harley Flanders,
**Differential Forms with Applications to the Physical Sciences**, Academic Press, New York, 1963; Dover, New York, 1989.*Excellent but somewhat dated introduction to differential forms; only covers the positive definite case.* - Richard L. Bishop and Samuel I. Goldberg,
**Tensor Analysis on Manifolds**, Macmillan, New York, 1968; Dover, New York, 1980.*Somewhat more sophisticated; a good reference for tensors.* - Robert H. Wasserman,
**Tensors and Manifolds**, Oxford University Press, Oxford, 1992.*A more readable version of Bishop and Goldberg; unfortunately not cheap.* - David Bachman,
**A geometric approach to differential forms**, Birkhäuser, Boston, 2006.*Very readable math text.* - David Lovelock and Hanno Rund,
**Tensors, differential forms, and variational principles**, Wiley, New York, 1975; Dover, New York, 1989.*Another inexpensive Dover reprint, covering similar material from a slightly different point of view.* - Hwei Hsu,
**Vector Analysis**(Chapter 10 only), Simon and Schuster Technical Outlines, 1969.*A sort of Schaum outline for differential forms.* - H. M. Schey,
**Div, Grad, Curl, and All That**, Norton, New York, 1973 (2nd edition: 1992; 3rd edition: 1997; 4th edition: 2005)*Excellent informal introduction to the geometry of vector calculus.*

- Gabriel Weinreich,
**Geometrical Vectors**, University of Chicago Press, Chicago, 1998.*A nice (if idiosyncratic), geometrical description of differential forms without ever using those words.* - Barrett O'Neill,
**Elementary Differential Geometry**, Academic Press, New York, 1966 (2nd edition: 1997).*Standard, fairly readable introduction to differential geometry in ordinary Euclidean 3-space. Uses differential forms extensively.* - Richard S. Millman and George D. Parker,
**Elements of Differential Geometry**, Prentice-Hall, Englewood Cliffs, NJ, 1977 (2nd edition: 1997).*Good undergraduate text covering similar material to the above. Does not use differential forms.* - Barrett O'Neill,
**Semi-Riemannian Geometry**, Academic Press, New York, 1983.*Graduate math text. The best available treatment of differential geometry without the usual assumption that the metric is positive definite.* - William M. Boothby,
**An Introduction to Differentiable Manifolds and Riemannian Geometry**, Academic Press, New York, 1986.*Fairly readable graduate math text. Good but brief treatment of differential forms and integration, but emphasis is on Lie groups.* - Manfredo Perdigão do Carmo,
**Riemannian Geometry**, Birkhäuser, Boston, 1992.*Quite readable math text, but no discussion of differential forms.* - Michael Spivak,
**A Comprehensive Introduction to Differential Geometry**, (5 volumes), Publish or Perish, Houston, 1970-1975 (2nd edition: 1979).*Everything you ever wanted to know, and then some, but not easy to read.* - Charles W. Misner, Kip S. Thorne, John Archibald Wheeler,
**Gravitation**, Freeman, San Fransisco, 1973.*Don't underestimate this classic! Chapter 4 has a nice introduction to differential forms, including great pictures and a discussion of electromagnetism. Part III also discusses the differential geometry needed for relativity.*