禅宗 in Chinese / Japanese...

禪宗 is one way to title “Zen Buddhism.” Because the original pronunciation of Zen in Chinese is Chan, you'll also see this expressed as Chan Buddhism.

From the Buddhist Dictionary:
The Chan, meditative or intuitional, sect is usually said to have been established in China by Bodhidharma, the twenty-eighth patriarch, who brought the tradition of the Buddha-mind from India. This sect, believing in direct enlightenment, disregarded ritual and sūtras and depended upon the inner light and personal influence for the propagation of its tenets, founding itself on the esoteric tradition supposed to have been imparted to Kāśyapa by the Buddha, who indicated his meaning by plucking a flower without further explanation. Kāśyapa smiled in apprehension and is supposed to have passed on this mystic method to the patriarchs. The successor of Bodhidharma was 慧可 Huike, and he was succeeded by 僧璨 Sengcan, 道信 Daoxin, 弘忍 Hongren, 慧能 Huineng, and 神秀 Shenxiu, the sect dividing under the two latter into the southern and northern schools: the southern school became prominent, producing 南嶽 Nanyue and 靑原 Qingyuan, the former succeeded by 馬祖 Mazu, the latter by 石頭 Shitou. From Mazu's school arose the five later schools.