These notes were developed as a supplement to a course on Differential Geometry at the advanced
undergraduate, first year graduate level, which the author has taught for several years. There are
many excellent texts in Differential Geometry but very few have an early introduction to differential
forms and their applications to Physics. It is the purpose of these notes to bridge some of these
gaps and thus help the student get a more profound understanding of the concepts involved. When
appropriate, the notes also correlate classical equations to the more elegant but less intuitive modern
formulation of the subject.
These notes should be accessible to students who have completed traditional training in Advanced
Calculus, Linear Algebra, and Differential Equations. Students who master the entirety of this
material will have gained enough background to begin a formal study of the General Theory of
Relativity.