The Suda says this about him.
While Anacreon himself touched on many subjects in his poetry, his songs of wine, women and song made such an impression that anonymous poets took to writing poems on these subjects in the stereotyped Anacreontic meters. Many of the poems were quoted by various authors, but the collection we know as the Anacreontics today comes from the Palatine Anthology.
Anacreontics. I number the poems according to the 1993 Teubner edition edited by M.L. West. The poems themselves come from Tyler and Smyth. Bergk's numbers are in parentheses.