This document presents a study of the contrapuntal lines in the compound melodies of the first three of Telemann's 12 Fantasias for Solo Flute. Each one of Telemann's Fantasias has its own character and form, and each is a complete work in itself. The analysis of its implicit harmonies and compound lines, extrapolating them into independent voices, provides a greater comprehension of its counterpoint, leading to a more consistent and clear performance of this repertoire. The style of each Fantasia and its movements is also examined to facilitate understanding of how to perform these pieces in a historically accurate manner. The performance and ornamentation suggestions given here follow Telemann's own ideas and format presented in his Methodical Sonatas. Telemann's 12 Fantasias are some of the most representative works from the repertoire for solo flute music of the 18th century. Telemann, a flutist himself, is one of the few composers of his time to write fugues, a passacaglia, and a French overture for solo flute. Indeed, this cycle of pieces was written specifically for the flute, and its importance in the repertoire can be likened to Bach's "Well Tempered Clavier" for keyboard instruments. There is no question about the pedagogical importance of this set of pieces, suitable for beginners to professional flutists.