Themes
Who moves last
The player unable to move loses. That single convention generates the whole theory, and reversing it — misère play — destroys almost all of it.
The sum is the object
Real positions break into independent parts that are played at once. Adding games up is not a technique within the theory; it is what the theory is for.
Not every game is a number
Some positions are worth a half or a quarter. Others are worth something no number can express, and the ones that are not numbers are where the subject becomes interesting.
The value is computable
A position's worth is not estimated. It is a symbolic object obtained by recursion, reduced to a canonical form, and comparable exactly with any other.
Play it and lose
The strongest argument this subject can make is to state the winner before the reader starts, and then be right. Optimal play falls out of the value; it is not a heuristic.
Small things decide
Infinitesimals are smaller than every positive number and are not zero. In a close game they are the whole margin, which is why the theory bothers with them.
The theory runs out
Misère play, loops and computational hardness each break something essential. Knowing which of the three is biting is most of knowing where a game stands.