It is often asserted that the $j$-invariant was first introduced by Felix Klein. Is there any evidence for this claim? What works of Felix Klein do deal with it? What is the origin of the symbol $j$ used for it? Where it had first appeared?
Felix Klein, Über die Transformation der elliptischen Funktionen und die Auflösung der Gleichungen fünften Grades, Math. Ann. 14, 111-172 (1878-1879).
There is also a slightly earlier brief note in Italian, Sull' equazioni dell' Icosaedro nella risoluzione delle equazioni del quinto grado, Rendiconti Reale Istituto Lombardo, Serie 2, vol. 10, p. 253-255 (1877).
Dedekind may have gotten there first, see Dedekind or Klein (p. 67).
Notation: Klein used capital $J$, there is a factor 1728 difference with the $j$-invariant. (Read more about the origin of this factor.)