This book is intended as a textbook for an undergraduate course on
algebra. In most universities a detailed study -of abstract algebraic
systems commences in the second year. By this time the student has
gained some experience in mathematical reasoning so that a too
elementary book would rob him of the joy and the stimulus of using his
ability. I tried to make allowance for this when I chose t4e level of
presentation. On the other hand, I hope that I also avoided discouraging
the reader by demands which are beyond his strength. So, the first
chapters will certainly not require more mathematical maturity than can
reasonably be expected after the first year at the university. Apart
from one exception the formal prerequisites do not exceed the syllabus
of an average high school. As to the exception, I assume that the reader
is familiar with the rudiments of linear algebra, i. e. addition and
multiplication of matrices and the main properties of determinants. In
view of the readers for whom the book is designed I felt entitled to
this assumption. In the first chapters, matrices will almost exclusively
occur in examples and exercises providing non-trivial instances in the
theory of groups and rings. In Chapters 9 and 10 only, vector spaces and
their properties will form a relevant part of the text. A reader who is
not familiar with these concepts will have no difficulties in acquiring
these prerequisites by any elementary textbook, e. g. [10].
