- 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.
