Symmetries often allow us to simplify the PDE dynamics that could be enigmatic in general, revealing the hidden structures the dynamics of our interest particularly bears. By imposing the $m$-fold symmetry on certain singular vortex patches within the 2D Euler system, we prove the global well-posedness of such patches in the H"older spaces for $mgeq 3$. This lecture is to revisit the existing result of Mem. Amer. Math. Soc. 283(1400):1–102 (2023) by T. Elgindi and I.-J. Jeong in detail with the core concepts.