The Fourier transform is used in many instrumental techniques, including infrared spectroscopy, NMR, and mass spectrometry. Although most instruments perform this mathematical technique transparently, an understanding of how it works is important. This understanding will help instrument users set appropriate parameters, appreciate the limitations of an instrument, and obtain better spectra. This document simultaneously introduces students to how the Fourier transform works and how various instrument parameters affect the results of the Fourier transform. Waveforms are produced and integrated using sine waves, cosine waves, and simple functions. The fast Fourier transform is used with simulated data to introduce students to the relationship between the signal waveform and the signal frequency of a spectrum. Students are then led to the concepts of dwell time and resolution through a series of interactive exercises. The document ends with an introduction to the Fourier transform of decaying signals. Students and teachers may use IntroFourierTransform.mcd as written, or teachers may remove some graphs to increase discovery learning and class discussion. IntroFourierTransform.mcd includes substantial student interaction by changing variables and written reflection exercises. The companion document, LectureIntroFT.mcd, designed for instructors to use interactively during lecture, is the abbreviated version of IntroFourierTransform.mcd. These Mathcad documents build on previously published work, Using Mathcad to Teach Instrumental Techniques; J. Chem. Educ. 1998, 75, 375.