This first part of a two-volume set offers a modern account of the
representation theory of finite dimensional associative algebras
over an algebraically closed field. The authors present this topic
from the perspective of linear representations of finite-oriented
graphs (quivers) and homological algebra. The self-contained
treatment constitutes an elementary, up-to-date introduction to the
subject using, on the one hand, quiver-theoretical techniques and,
on the other, tilting theory and integral quadratic forms. Key
features include many illustrative examples, plus a large number of
end-of-chapter exercises. The detailed proofs make this work
suitable both for courses and seminars, and for self-study. The
volume will be of great interest to graduate students beginning
research in the representation theory of algebras and to
mathematicians from other fields.
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