The Climber is a Manga/Manhwa/Manhua in english language, Adventure series, english chapters have been translated and you can read them here. You are reading chapters on www.mgeko.nl fastest updating comic site. The Summary is

From Stiletto Heels: On his first day of transferring to a new high school, a loner named Mori Buntarou, is cajoled by a classmate into climbing the school building. Despite knowing that one misstep could send him spiraling to his death, he moves forward, and upon finally reaching the top, Mori experiences a sense of fulfillment. That feeling, which seems to be telling him, "You're alive!" gives birth to an adrenaline for rock-climbing.