It is easy to explain the concept of a configuration of points and lines to
any ten-years-old youngster. Why then a book on this topic in a graduate
series? There are several good reasons:
First and foremost, configurations are mathematically challenging
even though easily accessible.
The study of configurations leans on many fields: classical geom-
etry, combinatorics, topology, algebraic geometry, computing, and
even analysis and number theory.
There is a visual appeal to many types of configurations.
There are opportunities for serious innovation that do not rely on
long years of preliminary study.
The truly remarkable aspect of configurations is the scarcity of results
in a field that was explicitly started well over a century ago, and informally
much earlier. One of the foremost aims of the present text is to make avail-
able, essentially for the first time ever, a coherent account of the material.
Historical aspects are presented in order to enable the reader to follow
the advances (as well as the occasional retreats) of the understanding of
configurations. As explained more fully in the text, an initial burst of en-
thusiasm in the late nineteenth century produced several basic results. For
almost a century, these were not matched by any comparably important
new achievements. But near the end of the last century it turned out that
the early results were incorrect, and this became part of the impetus for a
reinvigorated study of configurations.
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