I found this the most accessible of Nietzsche's books because it comes closest - especially in the second essay - to a straight exposition of his theories. The trouble is I liked it too much to paraphrase anything. I will only give one quote, which you will notice is excessively lengthy:Section 13: To give at least an idea of how uncertain, how supplemental, how accidental the “meaning” of punishment is, and how one and the same procedure can be employed, interpreted, adapted to ends that differ fundamentally, I set down here the pattern that has emerged from consideration of relatively few chance instances I have noted. Punishment as a means of rendering harmless, of preventing further harm. Punishment as recompense to the injured party for the harm done, rendered in any form (even in that of a compensating affect). Punishment as the isolation of a disturbance of equilibrium, so as to guard against any further spread of the disturbance. Punishment as a means of inspiring fear of those who determine and execute the punishment. Punishment as a kind of repayment for the advantages the criminal has enjoyed hitherto (for example when he is employed as a slave in the mines). Punishment as the expulsion of a degenerate element (in some cases of an entire branch, as in Chinese law: thus as a means of preserving the purity of a race or maintaining a social type.) Punishment as a festival, namely as the rape and mockery of a finally defeated enemy. Punishment as the making of a memory, whether for him who suffers the punishment = so called “improvement” - or for those who witness its execution. Punishment as payment of a fee stipulated by the power that protects the wrongdoer from the excesses of revenge. Punishment as a compromise with revenge in its natural state when the latter is still maintained and claimed as a privilege by powerful clans. Punishment as a declaration of war and a war measure against an enemy of peace, of the law, of order, of the authorities, whom, as a danger to the community, as one who has broken the contract that defines the conditions under which it exists, as a rebel, a traitor, and breaker of the peace, one opposes with the means of war.