In the summer of 1897, David Hilbert (1862-1943) gave an
introductory course in Invariant Theory at the University of
Gottingen. This book is an English translation of the handwritten
notes taken from this course by Hilbert's student Sophus Marxen. At
that time his research in the subject had been completed, and his
famous finiteness theorem had been proved and published in two
papers that changed the course of invariant theory dramatically and
that laid the foundation for modern commutative algebra. Thus,
these lectures take into account both the old approach of his
predecessors and his new ideas. This bridge from nineteenth to
twentieth century mathematics makes these lecture notes a special
and fascinating account of invariant theory. Hilbert's course was
given at a level accessible to graduate students in mathematics,
requiring only a familiarity with linear algebra and the basics of
ring and group theory. The text will be useful as a self-contained
introduction to invariant theory. But it will also be invaluable as
a historical source for anyone interested in the foundations of
twentieth-century mathematics.
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