Gokyo Shumyo, Section 1, Problem 19 / Solution

Black lives  

is the only conceivable move: no other move prevents White from linking up her stone inside the black group and destroying his eye space.

Main line  

White can make a ko shape but can't win the ko: black has enough liberties to squeeze. Black is alive.

Variation 1  

knows only one answer.

Question  

Question: What after White hanes immediately?
xela: I think black can simply block at a.

White hane, followup  

Here, a and b are miai, so black is alive.