Stüdlgrat

Scramble up boulder-y terrain to reach a chimney and then climb this (UIAA 2+) to reach blocky terrain just left of the ridge crest. Follow a natural line onto to the ridge crest and shortly after reaching it you'll find a yellow board right on the ridge crest, which marks the start of the real difficulties. This is the Frühstückplatz. 

Climb up a leftwards leaning ramp and continue up to 2 towers - bypass them both on the western side of the ridge, using a fixed cable (UIAA 3+) to get around the second one.

Scramble up just to the left of the ridge crest (UIAA 3) then drop off right before returning to the crest and climbing up to a slab (UIAA 3). Drop left off the ridge again before returning to the crest and then tackling a slab equipped with a cable (UIAA 3+) which leads rightwards and then comes back left to the crest. Climb the crest all the way to the summit via a series of ramps (UIAA 2) which are well equipped with various fixed gear.

From Stüdlhütte, you'll need to traverse to the base of the SW Ridge (Stüdlgrat). You can access the base by either getting on the Teischnitzkees Glacier or by staying on the rock bands to climber's right of the glacier. The rocks on the side are often loose, but it is possible to navigate to the base of the route without stepping on the glacier.

Various forms of fixed cables, fixed gear, and metal stakes. The route would take gear if roping up is desired.