If you’re truly interested in learning how to arrange flowers, probably one of the most challenging styles would be Ikebana, the ancient art of flower arranging. Ikebana’s Japanese characters translate to “living flowers” and it is considered a meditative art form.
Photo from Ikenobo Ikebana Society Los Angeles Chapter
I have always seen Ikebana as something like sculpting — just with flowers, branches and leaves. Western-style flower arrangements are more typically wild and full of blossoms, but Ikebana — like the related art of Bonsai — is more restrained and, some might argue, disciplined.