Gokyo Shumyo, Section 1, Problem 58 / Solution

Main line  

White enlarges her eye space with 1, then makes eye shape with 3. Incidentally, White 1 - Black 2 makes a notcher with code 411WN.

If White descends instead of move 3, then White is also alive. However this way is less good for White, as Black can profit by capturing some stones. See problem 28 in this series for details.

Continuation - variation 2  

White 2 at a also works.

Failure at 3  

The solid connection at 3 fails. It makes a 312NS notcher. How to attack this shape?

Failure at 3 (wrong punishment)  

Usually, there is death in the hane, but not here.

Failure at 3 (punished)  

This is the correct way to punish White: Black 1 strikes at the vital point, and if White 2, the hane kills.

Failure at 3 (punished)  

If White enlarges her EyeSpace, Black 3 and 5 prepare it to be almost filled with a killing shape.