These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate, first year graduate level, which by the author has taught for several years. There are many excellent good 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 concept involved. When appropriate, the notes also correlate classical equations to the more elegant but less intuitive modern formulation of the subject.