The term 'altermagnetism' has recently appeared in solid state physics referring to antiferromagnets possessing certain properties of ferromagnets such as non-zero linear magneto-optical effects. After an introduction to core-level spectroscopies and their ab initio simulation, I will present our recent calculation of circular dichroism in the X-ray absorption on MnTe films using the dynamical mean-field theory. I will discuss the symmetry aspects of altermagnetism as well as pros and cons of the X-ray spectroscopy for their investigation.