It is well known that using the hot water tap in one's home or elsewhere on Shabbos is forbidden. As one removes hot water from the tank, cold water immediately rushes in and is cooked.  AMNON18 is designed in such a way that you can use hot water on Shabbat & Yom Tov. Keeping the temperature of the water in the hot water tank below 'yad soledes', which is the minimum temperature required for cooking. Therefore, as one removes hot water, the cold water rushing into the tank is never halachically cooked but heated, even though it is very warm. Nonetheless, 4 issues need to be dealt with. 1] As cold water rushes into the hot water tank, the temperature decreases and eventually it will cause the fire or heating element to turn on and heat up the water to the desired temperature. It is questionable if one may cause this to happen, even though it is an indirect result of one's actions. Therefore, the Amnon 18 is designed to never allow the fire to turn on as a result of your actions. Rather, the fire will turn on at random intervals. Once it is on, it will remain on until the desired temperature is reached, using sensitive digital sensors. This way, one never causes any ignition on Shabbos. [There is also an option for the fire to also turn off at set intervals]. Additionally, the Amnon 18 has a safety feature called the "mashgiach valve". If the water in the tank ever happens to reach above the desired temperature, the sensors will immediately react and the hot water valve will automatically shut. This way one can not take out any hot water until the tank cools down. Furthermore, there is a mixing pump that is constantly causing movement of water in the tank. This ensures that the temperature towards the top of the tank will basically be the same as the temperature at the bottom of the tank. 2] Another issue is that of the Rabbinic prohibitions of "shehiya" and chazara". It is known that one may not place even cooked food or hot liquids in a place that is meant for cooking, as it appears one is doing an act of cooking. When one causes col water to enter the tank, he has "placed" water in the tank, which is a place where water cooks. However, as explained at length in the article, this does not pose a problem by the Amnon 18, since the prohibition applies only to a place where the current temperature is above 'yad soledes' and has the ability to cook. With the Amnon 18, the water will never reach that temperature, as explained above. [see the article where additional factors are discussed]. 3] The last issue is that of the digital sensors and the digital display. Attached to the hot water tank is the Amnon 18 device which has a digital display screen conveying the current temperature of the hot water tank. As one uses 'hot' water, cold water rushes into the tank and slowly starts to cool down the water inside. After some time, this change in temperature will display on the screen. Additionally, the electronic sensors themselves calculate the water temperature by means of slight changes in voltage. Therefore, it's possible that every time the hot water tap is opened, one is affecting the display, as well as the workings of the sensor. However, as explained at length in the article, these changes do not occur immediately and are classified as 'Grama'. Since one does not intend for any of these changes, it is considered 'Psik reishe' with a grama and is permitted, along with other considerations. [Additionally, there is an option on the device called 'Magen Avraham'. Choosing this option means that as long as the fire or heating element is on, the 'mashgiach valve' is closed and one can not take hot water. During the time when the fire is off and one is able to take hot water, the display will not show the temperature. Rather, it will just display the word "standby", thereby avoiding any question of affecting the display.] 4] Even after concluding that there is no prohibition in opening the hot water tap using the Amnon 18, there is still the question of how exactly one may use that 'hot' water. Chazal enacted a gezera forbidding showering/bathing on Shabbos and Yom tov due to various concerns. This enactment includes water that is not yad soledes, but is still 'hot'. It is debatable whether one may use lukewarm water. Also, Askenazi custom forbids showering the majority of one's body even in cold water. Even washing one's hands or other part of the body with 'hot' water is generally forbidden on Shabbos. The article on showering with the Amnon 18 discusses all this and more. Using 'hot' water (obviously referring to water that is not yad soledes) to shower the majority of ones body on Shabbos is forbidden. Using 'hot water' to wash ones hands (or minority of one's body) on Shabbos is a question, and there is room for leniency. Other details, including showering the full body, are discussed in the article.