Fill outside liberties first

Capturing race  

In this race to capture, the circled points are inside liberties and the squared ones are the outside liberties. Black must play an outside liberty first to make seki. Playing an inside liberty will kill his own stones. White may disobey and fill an inside liberty first if it's her turn, but it's a bad habit.

However, not all capturing races are that clear-cut. Sometimes what looks like an inside liberty turns out to be a move that generates more outside liberties, thus winning the race. See diagonal to the first line.

Capturing race  

Perhaps the definition is a little bit vague for you? If we consider the and chains, then the outside liberties for the chain is marked b, then outside liberties for the chain is marked w, and the inside liberties (or shared liberties) of the and chains are marked s. --unkx80

Geoff Wedig: Yes, you're missing something: a key fact from the definition. The 'outside' and 'inside' refer to the groups that have potential to be captured. Other groups are part of the surroundings. That is why the squared points aren't inside liberties. They aren't shared by the (potentially) capturable groups.