The first point is more complicated than it seems. Black should play

in sente.
$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X O . . . X . . O X X O X . |
$$ | . X X X X X O . . X O X . . O X O X . |
$$ | . X O O O 1 . . O O O O O . . X O X . |
$$ | c O O . . 2 O . . X O X O . O X X O . |
$$ | d a X b . . . . . . O X O O X . X O . |
$$ | . . . . O . . O . O X X X X X X X O . |
$$ | . . . . . . X X O . O X O O X X X . . |
$$ | . . O O . X . . X O . O . . O . . . . |
$$ | . . . , . O X X . , O . . . . , X . . |
$$ | . . O O . X O X . O X O . . . . . . . |
$$ | . X X X X . . . . . X O . O . O O . . |
$$ | . O . . . O . . . . . X . . . X . . . |
- Click Here To Show Diagram Code
[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X O . . . X . . O X X O X . |
$$ | . X X X X X O . . X O X . . O X O X . |
$$ | . X O O O 1 . . O O O O O . . X O X . |
$$ | c O O . . 2 O . . X O X O . O X X O . |
$$ | d a X b . . . . . . O X O O X . X O . |
$$ | . . . . O . . O . O X X X X X X X O . |
$$ | . . . . . . X X O . O X O O X X X . . |
$$ | . . O O . X . . X O . O . . O . . . . |
$$ | . . . , . O X X . , O . . . . , X . . |
$$ | . . O O . X O X . O X O . . . . . . . |
$$ | . X X X X . . . . . X O . O . O O . . |
$$ | . O . . . O . . . . . X . . . X . . . |[/go]
If White doesn't answer with

then Black can play a. If White responds with c or d then Black b. The variations are a bit complicated but normally Black can threaten to capture white stones and then connect to a living group to save his three stones. So Katago prefers white to answer Black a with White b, and then Black can connect with c.
Then Black should play

in sente. If White doesn't respond with

then Black can play a.
$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X O . . . X . . O X X O X . |
$$ | . X X X X X O . a X O X . . O X O X . |
$$ | . X O O O 1 3 4 O O O O O . . X O X . |
$$ | . O O . . 2 O . . X O X O . O X X O . |
$$ | . . X . . . . . . . O X O O X . X O . |
$$ | . . . . O . . O . O X X X X X X X O . |
$$ | . . . . . . X X O . O X O O X X X . . |
$$ | . . O O . X . . X O . O . . O . . . . |
$$ | . . . , . O X X . , O . . . . , X . . |
$$ | . . O O . X O X . O X O . . . . . . . |
$$ | . X X X X . . . . . X O . O . O O . . |
$$ | . O . . . O . . . . . X . . . X . . . |
- Click Here To Show Diagram Code
[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X O . . . X . . O X X O X . |
$$ | . X X X X X O . a X O X . . O X O X . |
$$ | . X O O O 1 3 4 O O O O O . . X O X . |
$$ | . O O . . 2 O . . X O X O . O X X O . |
$$ | . . X . . . . . . . O X O O X . X O . |
$$ | . . . . O . . O . O X X X X X X X O . |
$$ | . . . . . . X X O . O X O O X X X . . |
$$ | . . O O . X . . X O . O . . O . . . . |
$$ | . . . , . O X X . , O . . . . , X . . |
$$ | . . O O . X O X . O X O . . . . . . . |
$$ | . X X X X . . . . . X O . O . O O . . |
$$ | . O . . . O . . . . . X . . . X . . . |[/go]
Next comes this sequence:
$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X O . . . X . . O X X O X . |
$$ | . X X X X X O . . X O X . . O X O X . |
$$ | . X O O O 1 3 4 O O O O O . . X O X . |
$$ | . O O . . 2 O . . X O X O . O X X W . |
$$ | . . X . . . . . . . O X O O X . X W . |
$$ | . . . . O . . O . O X X X X X X X W . |
$$ | . . . . . . X X O . O X O O X X X . . |
$$ | . . O O . X . . X O . O . . O . . a . |
$$ | . . . , . O X X . , O . . . . , X . . |
$$ | . . O O . X O X . O X O . . . . . 5 . |
$$ | . X X X X . . . . . X O . O . O O 6 . |
$$ | . O . . . O . . . . . X . . . X 7 b . |
$$ | . X X X . . . X . . X . . X . X O . . |
$$ | . O X O . . O . . X . . . . . X O . . |
$$ | . O X O . . . X X O . . . X O O X . . |
$$ | . . O O . . O O O . . O . . X X X . . |
$$ | . . . . . . . . . . . . . O . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X O . . . X . . O X X O X . |
$$ | . X X X X X O . . X O X . . O X O X . |
$$ | . X O O O 1 3 4 O O O O O . . X O X . |
$$ | . O O . . 2 O . . X O X O . O X X W . |
$$ | . . X . . . . . . . O X O O X . X W . |
$$ | . . . . O . . O . O X X X X X X X W . |
$$ | . . . . . . X X O . O X O O X X X . . |
$$ | . . O O . X . . X O . O . . O . . a . |
$$ | . . . , . O X X . , O . . . . , X . . |
$$ | . . O O . X O X . O X O . . . . . 5 . |
$$ | . X X X X . . . . . X O . O . O O 6 . |
$$ | . O . . . O . . . . . X . . . X 7 b . |
$$ | . X X X . . . X . . X . . X . X O . . |
$$ | . O X O . . O . . X . . . . . X O . . |
$$ | . O X O . . . X X O . . . X O O X . . |
$$ | . . O O . . O O O . . O . . X X X . . |
$$ | . . . . . . . . . . . . . O . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

is very big because White playing there is sente (threatens to save the three marked stones). White responds with

(if White plays elsewhere then Black

and

is at

anyway). One reason why

is big is that, besides reducing Black's corner, it threatens the reduction move a. So after a sequence starting with a, Black will close the corner with b.
Another worthwhile and simple sequence for Black later: close territory while pressing White down to the second line in sente.
$$Bc
$$ | . X X X X . . . . . X O . O . O O O . |
$$ | . O . . . O . . . . . X . . . X X X . |
$$ | . X X X . . . X . . X . . X . X O . . |
$$ | . O X O . . O . . X . . . . . X O . . |
$$ | . O X O . . . X X O 3 7 . X O O X . . |
$$ | . . O O . . O O O 4 5 O 1 . X X X . . |
$$ | . . . . . . . . . . 6 8 2 O . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$Bc
$$ | . X X X X . . . . . X O . O . O O O . |
$$ | . O . . . O . . . . . X . . . X X X . |
$$ | . X X X . . . X . . X . . X . X O . . |
$$ | . O X O . . O . . X . . . . . X O . . |
$$ | . O X O . . . X X O 3 7 . X O O X . . |
$$ | . . O O . . O O O 4 5 O 1 . X X X . . |
$$ | . . . . . . . . . . 6 8 2 O . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]