This thesis develops an analytical approach to the instrumental music of Orlando Gibbons (1583-1625) based on close readings of historical theory sources, primarily by Thomas Morley, John Coprario and Thomas Campion. Music of the early seventeenth century can be difficult to analyse, since it falls between the more extensively studied and theorised practices of classic vocal polyphony and common-practice tonality. Although English music theory of this period is recognised as strikingly modern in many respects, innovative aspects of English compositions from the same period receive little attention in standard accounts of the seventeenth century. I argue that concepts taken from this body of historical theory provide the basic terms of a technical vocabulary for analysis, which should be further refined through application to real compositions. Successive chapters deal with common counterpoint models or patterns, imitative invention and disposition, cadential progressions, and overall tonal structure. I argue that these analyses show Gibbons's music to be a contribution to new ways of conceiving of instrumental polyphony and tonal structure, which deserves re-evaluation in the context of broader seventeenth-century trends. In particular, Gibbons's use of extended cadential expectations as an expressive element, fascination with sequential progressions, and sectional structuring by harmonic area have clear parallels with later practices. At the same time, early seventeenth century style allows the composer considerably more freedom of harmonic procedures and implications than the musical styles which immediately followed it. Analysis grounded in historical theory provides the best approach to understanding and appreciating this unique musical language.