One of the simple and most widely used microwave antennas is the horn as a feed element for large radio telescopes, satellite tracking, and communication reflector, which are found installed throughout the world. In addition to its utility as a feed for reflectors and lenses, it is a common element of phased arrays and serves as a universal standard for calibration and gain measurement of other high gain antennas. Its widespread applicability stems from its simplicity in construction, ease of excitation, large gain, wide-band characteristics, and preferred overall performance. An electromagnetic horn can take many different forms, such as basic pyramidal, conical, corrugated, double-ridged, and dual polarized horns, as well as horns with lens and so on. The horn is nothing more than a hollow pipe of different cross-sections, which has been tapered to a larger opening aperture. This chapter explains the fundamentals of the pyramidal horn antenna in detail using aperture field method. Numerical and measured examples, are also shown.