I try to study the Lindelöf number of topological space. Are there some classical books or papers or useful links on this? Thanks!
The classic reference for cardinal functions in topology is István Juhász, Cardinal functions in topology, Math. Centre Tracts 34, Amsterdam, 1971. It was superseded by his Cardinal functions in topology: ten years later, Math Centre Tracts 123, Amsterdam, 1980, with a second printing in 1983. Both are freely available in PDF here: search on cardinal functions in the Title field. (There are also direct links to the PDFs here.) The articles Cardinal Functions I and Cardinal Functions II by Richard Hodel and István Juhász, respectively, in the Handbook of Set-Theoretic Topology, Kenneth Kunen and Jerry E. Vaughan, eds., North-Holland, 1988, are also worth a look. All of these have copious references.
Of course all of those references are at least $25$ years old; a search on Lindelöf degree and Lindelöf number will turn up a great deal of more recent material on this and related topics. But they should still be a useful starting point.