The title above is strictly rhetorical: in go one cannot live without liberties. In fact, the essence of the game depends upon at least two liberties (eyes) being accessible to one's groups. And one must take care that one avoids a shortage of liberties that will result in the death of one's stones. Beginners take a great step forward in understanding when they can recognize the implications of a shortage of liberties. If one can learn to avoid such situations while utilizing a shortage of liberties against one's opponents, one will notice one's strength developing measurably.
The problem above is one created by the late Maeda Nobuaki 9 dan, who was known as the "god of tsume-go (life and death problems)" for the elegance and fecundity of his imagination. As in many of his problems, one must take advantage of the adversary's shortage of liberties while avoiding a shortage of one's own. Analyzing problems such as this one helps one to develop reading skills that are necessary to improvement. Please take a moment to examine this one before reading to the analysis following.
Interestingly, there are actually only four points to play in this corner: the moves a through d in Diagram 1. Despite this fact, beginners will often have difficulties in solving it. That is because of blind spots in beginners' reading ability. It is for just this reason that life and death problems are valuable learning tools.