Fux divided Gradus ad Parnassum into two parts:
"In the first part, Fux presents a summary of the theory on Musica Speculativa, or the analysis of intervals as proportions between numbers. This section is in a simple lecture style, and looks at music from a purely mathematical angle, in a theoretical tradition that goes back, through the works of Renaissance theoreticians, to the Ancient Greeks. The words of Mersenne, Cicero and Aristotle are among the references quoted by Fux in this section.
"The second part, on Musica Pratica [or practical performance], is the section of this treatise where the author presents his instruction on counterpoint, fugue, double counterpoint, a brief essay on musical taste, and his ideas on composing Sacred music, writing in the Style A Cappella and in the Recitativo Style. This part is in the form of a dialog, between a master (Aloysius, Latin for Luigi, who is meant to represent Palestrina's ideas) and a student, Josephus, who represents Fux himself, a self-admitted admirer of Palestrina. At the outset Fux states his purpose: "to invent a simple method by which a student can progress, step by step, to the heights of compositional mastery..." and he gives his opinion of contemporary practice: "I will not be deterred by the most passionate haters of study, nor by the depravity of the present time." He also states that theory without practice is useless, thus his book stresses practice over theory" (Wikipedia article on Johann Fux, accessed 09-04-2010).
Leopold Mozart is said to have taught his son Wolfgang from Gradus ad Parnassum. JS Bach and Beethoven both held it in great esteem, and Haydn meticulously worked out each of its exercises. Translated into the vernacular, Fux's work remains useful for the study of counterpoint. See The Study of Counterpoint from Johann Joseph Fux's Gradus ad Parnassum. Translated and edited by Alfred Mann (1943, 1965). (The paperback copy that I consulted was from its 34th printing.)