What is the meaning of the pair Apollonian and Dionysian in Nietzsche's philosophy of art? In which work does Nietzsche expand his view?
The text is The Birth of Tragedy from the Spirit of Music, an 1872 work of dramatic theory.
The Apollonian (according to Nietzsche's usage of the term) is the principle of the individualization (Principium Individuationis), it represents the social/historical force that creates the society, the individual, the personality, the civilization, consciousness etc.
It is based on Logos, reason, clarity etc and represents the ability of the individual in the progress of human society to create a rational image of the self inside the world. The main aesthetic element is the clear form.
Just as in a stormy sea, unbounded in every direction, rising and falling with howling mountainous waves, a sailor sits in a boat and trusts in his frail barque: so in the midst of a world of sorrows the individual sits quietly supported by and trusting in his principium individuationis. Indeed, we might say of Apollo, that in him the unshaken faith in this principium and the quiet sitting of the man wrap therein have received their sublimest expression; and we might even designate Apollo as the glorious divine image of the Principium Individuationis, from out of the gestures and looks of which all the joy and wisdom of "appearance," together with its beauty speak to us.
– The Birth of Tragedy, Friedrich Nietzsche Russell & Russell 1964 p25)
The Apollonian is contrasted with the Dionysian, that represents the chthonic (χθόνιο) (ground-earth) element, the incapability of creating a rational view of the world, the instinct.
One can observe the difference of these two elements as expressed in art forms. Some of those incorporate both elements but some represent more one or the other.
Nietzsche develops his thoughts on European art in his essay from 1872 The Birth of Tragedy from the Spirit of Music. Already in the first sentence he introduces his thesis that any development of art is bound to the pair Apollonian and Dionysian. He introduces both terms as a pair of opposed drives. As a first approximation he relates them to the two human states of dream and frenzy (German: Rausch).
For me it is rather difficult to follow Nietzsche's text and to make any sense from the big words in his general statements. The author asserts far reaching claims, makes comparisons, but he does not give arguments. He alludes to his precursors in philosophy of art, in particular to Friedrich Schiller. The terms Apollonian and Dionysian had been introduced before by the German philosopher Friedrich Schelling in an essay from 1795/96 Über das Studium der Griechischen Poesie.
The essay is one of the earliest works of Nietzsche. It results from his time as professor of classical philology and from his adoration of Richard Wagner, who at this time was his mentor in arts.
It is well known that the essay was also his swan song in this discipline. After publication his reputation as classical philologists was ruined and Nietzsche started his career as philosoph. Later Nietzsche added a second preface entitled Attempt of self-criticis (German: Versuch einer Selbstkritik) where he pulls the book to pieces.