Climb to the Ritter-Banner saddle as described on the Banner Peak page. Ice axe and crampons are almost always required for this route.
Banner Peak is an easy 30-45 minute scramble from the saddle. If you haven't been to the summit before and if you have the extra energy, it is well worth a visit. There is an outstanding view of Ritter's North Face from the summit.
There are several routes that can be followed up the North Face. Two will be described here, the classic Muir route, and the easier Right Hand Chute, well described in Jim Ramaker's excellent trip report on Climber.org. From the Banner-Ritter saddle, head south onto the North Glacier. Ice axe and crampons are usually needed. In mid to late summer the top portion of the Glacier can be quite icy - extra caution advised. I found this the most difficult challenge of the entire route.
The classic route goes up the central chute directly above the apex of the Glacier. This chute is steeper than the alternative, but still class 3. Near the top of the chute, but before reaching the ridge above, traverse left into the next chute on an uneven ledge. Climb a narrow, steep ramp about 5 ft wide that rises diagonally up to the left, intersecting the NE Ridge. This ramp may be filled with snow, but the rock edge to the left of the ramp can be climbed to avoid it. Scramble the remaining 100ft or so of the NE Ridge to the summit.
The easiest route climbs the Right Hand Chute. From about 20 feet below the apex of the Norht Glacier, head right for a ramp that leads to the Right Hand Chute. This is mostly a steep class 2 climb which can easily be made into class 3 by the many choices you encounter in climbing the chute. At the top of the chute, follow the NW Ridge up for several hundred feet until progress is blocked by gendarmes. You can then drop down to the classic route for the finish to the NE Ridge, or bypass the gendarmes on the right and find a broad class 2-3 chute on the west side. Follow the chute to the summit.
Axe and crampons required most times for the North Glacier.
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