As per the main page, start at the Argentiere hut (2771m, CAF, Tel: 50 53 16 92). The hut is open from the 15th March until the 15th September and serves food.
(To write this I refered to The Alpine Club guide book: Mont Blanc Massif Vol II, Lindsay Griffin).
This is the normal route and it was the route of the first ascent of the mountain in 1876 by Javelle, Turner, Moser and Tournier. It is now, however, normally used only in descent after a traverse over from the North ridge. From the Argentiere hut descend to the argentiere glacier and follow it up until the 'junction' with the Tour Noir Glacier which leads up North East. Ascend the cravassed glacier carefully, keeping to the true right (north) to avoid the largest cravasses. As the slope steepens and you approach the obvious col on the ridge branch left to the smaller, higher, col known as the 'passage d'Argentiere'.
From this col ascend the ridge, passing any difficulties on the left until you hit a large pionted gendarme. Above this the ridge becomes steeper and although it is a possible ascent route, the classic route traverses right here across the South Face on narrow ledges over sometimes loose rock. There are some pitons in place here. Traverse 80m to a rock rib and ascend this at first via a steep but usually snow free couloir (move of II+, but seems harder). This leads to a ridge and the angle soon decreases as you reach the col. The highest summit is the Northern one (on the right) and it takes ten minutes from the col.
The view from the top makes the climb thououghly worth while. You get an amazing 360 degree panorama, with Mt. Blanc to the south West, and Crand Combin and the Matterhorn to the East.
1: All the usual gear for crossing glaciers (1x Ice axe, crampons, rope, cravasse rescue knowledge).
2: Some extenders (quick draws).
3: A couple of slings each for running belays over spikes.
4: A few nuts and one or two camming devices (friends) - optional.
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