  The quasi-Lindel\"of property was first introduced by Arhangelski in
\cite{Arc}, as a strengthening of the weakly Lindel\"of property. However,
unlike Lindel\"of and weakly Lindel\"of spaces, very little is known about how
quasi-Lindel\"of spaces behave under the main topological operations, and how
the property relates to separation axioms. In the present paper, we look at
several properties of quasi-Lindel\"of spaces. We consider several examples: a
weakly Lindel\"of space which is not quasi-Lindel\"of, a product of Lindel\"of
spaces which is not even quasi-Lindel\"of, and a quasi-Lindel\"of space which
is not ccc. At the end, we pose some open questions.
