The really interesting and fundamental treatment of the concept of meme has to be found in the realm of cognitive evolutionary science. An interesting and very readable treatment can be found in From Bacteria to Bach and Back by Daniel C Dennett. He considers for example every lexical item ('word') a meme in the sense that it can be considered an element that reproduces in culture by 'infecting' cognitions analoge to but much faster than genes do.
Many linguists/cultural study scholars works in a less fundamental way with this concept. See for example [attachment] the collection of papers to which I was invited to contribute a chapter (although I hardly dare to say that I consider my chapter a contribution to meme theory :-( )
The word/concept meme was coined as a cultural analog to the gene. Nor entirely sure I remember correctly but I believe it was coined by Richard Dawkins. It is related to Lamarkian genetics except that it refers to the transmission and diffusion of knowledge. In addition to work by Dennett I would recommend Dawkins and Hoffstadter.