Argument of Knowledge - Definition
The notion of proofs (resp., argument) of knowledge was introduced in [GMR] (resp., [BCLL]), but the definition in both the papers is more intuitive than formal. Attempts were made at more formal definitions in [FFS] and [FS]. The culmination of these lines of work (I believe) is [BG], which is what I would recommend reading since (i) it post-dates the other works and (ii) it provides a good summary of the previous definitions (see Appendix A). [BG] focuses on proofs of knowledge, but the definitions for arguments of knowledge is similar (see §4.7).
Addendum. As @Yehuda Lindell points out, the textbook definition in [G] is worth looking into and it seems that the definition there closely follows [BG] (see the historical notes in §4.12.1).
[BCLL], Brassard, Crépeau, Laplante and Léger, Computationally Convincing Proofs of Knowledge, STACS'91
[BG] Bellare and Goldreich, On Defining Proofs of Knowledge, Crypto'92
Feige, Fiat and Shamir, Zero-knowledge proofs of identity, STOC'87
Feige and Shamir, Witness indistinguishable and witness hiding protocols, STOC'90
Goldwasser, Micali and Rackoff, The Knowledge Complexity of Interactive Proof-Systems, STOC'85
Goldreich, Foundations of Cryptography, Volume 1