¹The concept of the Seiberg-Witten curve was introduced in [2]. The concept of the ultraviolet curve, applicable in a general setting, can be traced back to [4], see Fig. 1 there. As also stated there, it was already implicitly used in [20, 21, 22]. In [8], the ultraviolet curve was used very effectively to uncover the duality of $\mathcal{𝒩}=2$ theories. Privately, the author often calls the ultraviolet curve as the Gaiotto curve, but this usage would not be quite fair to every party involved. In view of Stiegler’s law, the author could have used this terminology in this lecture note, but in the end he opted for a more neutral term ‘the ultraviolet curve’, which contains more scientific information at the same time. The author could have similarly used ‘the infrared curve’ for the Seiberg-Witten curve. As there is no bibliographical issue in this case, however, the author decided to stick to the standard usage to call it the Seiberg-Witten curve.