  Left-symmetric algebras have close relations with many important fields in
mathematics and mathematical physics. Their classification is very complicated
due to the nonassociativity. In this paper, we re-study the correspondence
between left-symmetric algebras and the bijective 1-cocycles. Then a procedure
is provided to classify left-symmetric algebras in terms of classification of
equivalent classes of bijective 1-cocycles. As an example, the 3-dimensional
complex left-symmetric algebras are classified.
