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The symbol ''<b>a</b>'' (the first letter of the word ''[[other|autre]]'', or "[[other]]") is one of the first [[algebraic]] [[sign]] which appears in [[Lacan]]'s [[Works of Jacques Lacan|work]], and is first introduced in 1955 in connection with [[schema L]].  It is always lower case and italicized to show that it denotes the [[little other]], in opposition to the capital '<b>A</b>' of the [[big Other]].  Unlike the [[big Other]], which represents a radical and irreducible [[big Other|alterity]], the [[little other]] is "the other which isn't another at all, since it is essentially coupled with the ego, in a relationship which is always reflexive, interchangeable."<ref>{{S2}} p.321</ref>  In [[schema L]], then, ''a'' and ''a''' designate indiscriminately the [[ego]] and the [[counterpart]]/[[specular image]], and clearly belong to the [[imaginary order]].

In 1957, when [[Lacan]] introduces the [[matheme]] of [[fantasy]] ('''$ <> <i>a</i>'''), ''a'' begins to be conceived as the [[object]] of [[desire]].  This is the [[imaginary]] [[part-object]], an element which is imagined as separable from the rest of the [[body]].  Lacan now begins to distinguish between ''a'', the [[object]] of [[desire]], and the [[specular image]], which he now symbolizes ''i(a)''.

In the seminar of 1960-1, [[Lacan]] articulates the ''[[objet (petit) a|objet petit a]]'' with the term ''[[agalma]]'' (a Greek term meaning glory, an ornament, an offering ot the gods, or a little statue of a god) which he extracts from [[Plato]]'s ''[[Plato|Symposium]]''.  Just as the ''[[agalma]]'' is a precious [[object]] hidden inside a relatively worthless box, so the ''[[objet (petit) a|objet petit a]]'' is the [[object]] of [[desire]] which we seek in the [[other]].<ref>{{S8}} p.177</ref>

From 1963 onwards, '''<i>a</i>''' comes increasingly to acquire connotations of the [[real]], although it never loses its [[imaginary]] status; in 1973 [[Lacan]] can still say that it is [[imaginary]].<ref>{{S20}} p.77</ref>  From this point on, ''[[objet (petit) a|a]]'' denotes the [[object]] which can never be attained, which is really the [[cause]] of [[desire]] rather than that towards which [[desire]] tends; this is why [[Lacan]] now calls it the "[[objet (petit) a|object-cause]]" of [[desire]].

''[[objet (petit) a|Objet petit a]]'' is any [[object]] which sets [[desire]] in motion, especially the [[partial object]]s which define the [[drive]]s.  The [[drive]]s do not seek to attain the ''[[objet (petit) a|objet petit a]]'', but rather circle round it.<ref>{{S11}} p. 179</ref>

In the [[seminar]]s of 1962-3 and of 1964, ''[[Objet (petit) a|objet petit a]]'' is defined as the leftover, the remainder ([[Fr]]. ''[[reste]]''), the remnant left behind by the introduction of the [[symbolic]] in the [[real]].  This is developed further in the [[seminar]] of 1969-70, in which [[Lacan]] elaborates his [[algebra|formulae]] of the [[four discourses]].  In the [[discourse]] of the [[master]], one [[signifier]] attempts to represent the [[subject]] for all other [[signifier]]s, but inevitably a [[surplus]] is always produced; this [[surplus]] is ''[[Objet (petit) a|objet petit a]]'', a [[surplus]] [[meaning]], and a [[surplus|surplus enjoyment]] ([[Fr]]. ''[[surplus|plus-de-jouir]]'').  This concept is inspired by [[Marx]]'s concept of [[surplus value]]; ''[[Objet (petit) a|a]]'' is the excess of ''[[jouissance]]'' which has no "[[use value]]" but persists for the mere sake of [[enjoyment]].