The most well-known and used wave for oceanographers and marine/harbour/coastal engineers is shown. Along with the simplifying hypothesies necessary for the calculation of the Airy wave, the consequent limitations on their use are also described. Simplified formulas for the dispersion equation in shallow and deep waters emerge easily through several practical cases together with solved explanatory problems. For the case of intermediate waters, some tables have been supplied with step-by-step instructions on how to utilize them. Other concepts such as the speed and trajectory of particles, as well as pressure, energy or power, are presented in a clear and simple way.