Is it permissible to take a beauty and makeup course to use its skills at home and for special occasions?

There is no impediment for a Muslim woman to learn the art of beautification to benefit herself or others, provided that it is regulated by Sharia controls. Thus, it is not permissible to beautify with what is forbidden, such as plucking eyebrows (namṣ), hair extensions (waṣl al-shaʿr), tattooing (washm), and teeth-filing (washr).