This book is concerned with one of the most fundamental questions of
mathematics: the relationship between algebraic formulas and geometric
images.
At one of the first international mathematical congresses (in Paris in
1900), Hilbert stated a special case of this question in the form of his
16th problem (from his list of 23 problems left over from the
nineteenth century as a legacy for the twentieth century).
In spite of the simplicity and importance of this problem (including its
numerous applications), it remains unsolved to this day (although, as
you will now see, many remarkable results have been discovered).