Since the publication of the Glimpses in 1998, I spent a considerable
amount of time collecting “mathematical pearls” suitable to
add to the original text. As my collection grew, it became clear that
a major revision in a second edition needed to be considered. In
addition, many readers of the Glimpses suggested changes, clarifi-
cations, and, above all, more examples and worked-out problems.
This second edition, made possible by the ever-patient staff of
Springer-Verlag New York, Inc., is the result of these efforts. Although
the general plan of the book is unchanged, the abundance
of topics rich in subtle connections between algebra and geometry
compelled me to extend the text of the first edition considerably.
Throughout the revision, I tried to do my best to avoid the inclusion
of topics that involve very difficult ideas.