The "Large Millimeter Telescope" (LMT), or "Gran Telescopio Milimetrico" (GTM), is a joint USA/Mexico Project and will be the world's largest short millimeter-wavelength (lambda = 1 to 3.4 mm) radio telescope. The large collecting area, equivalent to a circular aperture of 50 m diameter, and the high altitude (4600 m) site will allow the LMT/GTM to achieve unprecedented astronomical performance. The telescope will be equipped with state-of-the-art heterodyne (lambda = 3 mm) and bolometric (lambda = 1 mm) focal plane arrays which will make it a powerful high angular resolution mapping instrument. Here, we present the current status of the LMT/GTM Project and its primary astronomical performance specifications. We then describe the optical design of the telescope, including some important aspects related to the wobbling subreflector and to the reimaging optics. We also analyse some of the electromagnetic characteristics of the alternative telescope configurations, enclosed or open-air, that were considered before the final selection of an open-air telescope took place.