The ko variation  

The ko variation starts with the descent.

The ko variation, black backs off and tries to kill  

Suppose black just connects and doesn't want to fight it. Then the corner's not alive, right, black can easily reduce its eyespace? Unfortunately, black has a weakness they need to defend. The circled point would connect everything up instead.

W lives small variation 1: descend  

The other variation is pretty simple and starts with a connection, giving you a strong wall. I see two main variations, although more stuff could work if white has something on the outside in the right place. Most of the moves here seem natural so should be easy to memorize.

In this first variation, B0 could maybe be omitted depending on the local and ladder situation. You can handle the clamp as shown in the second diagram but it seems very uncomfortable depending on the side situations. Probably safe to just protect the cut.

W lives small variation 2: hane, black hanes later  

And white's alive. Basic tsumego: how does white respond if is at 9 instead?

W lives small variation 2: hane, black descends later  

Another variation where black descends, white follows, and black tries to kill. This is more complicated and likely still favorable for black, since white's 3-3 invasion here isn't particularly good in the first place. The general idea is white makes the 1-5 eye-making move sente.

cont.  

This comment is not related to the diagram at left, I just can't find how to get a paragraph below a preceding diagram? Also, if white makes an empty triangle instead, there's tons of variations, I think these are mostly bad for white though. Something similar to the ko is possible.

corner  

Given enough outside strength, Black can indeed kill.

corner  

it can become complicated