A pulsed terahertz (THz) wave with a frequency range from 0.1 THz to 10 THz is called a "T-ray." T-rays occupy a large portion of the electromagnetic spectrum between the infrared and microwave bands. However, compared to the relatively well-developed science and technology in the microwave, optical, and x-ray frequencies for defense and commercial applications, basic research, new initiatives and advanced technology developments in the THz band are very limited and remain unexplored. However, just as one can use visible light to create a photograph, radio waves to transmit music and speech, microwave radiation (MRI) or X-rays to reveal broken bones, T-ray can be used to create images or communicate information. This course will provide the fundamentals of free-space THz optoelectronics. We will cover the basic concepts of generation, detection, propagation, and applications of the T-rays, and how the up-to-date research results apply to industry. The free-space T-ray optoelectronic detection system, which uses photoconductive antennas or electro-optic crystals, provides diffraction-limited spatial resolution, femtosecond temporal resolution, DC-THz spectral bandwidth and mV/cm field sensitivity. Examples of homeland security and defense related projects will be highlighted.