  The duality cascade, and its dual description as string theory on the warped
deformed conifold, brings together several sophisticated topics, some of which
are not widely known. These lectures, which contain a number of previously
unpublished results, and are intended for experts as well as students, seek to
explain the physics of duality cascades. Seiberg duality is carefully
introduced, with detailed attention to the physical implications of duality
away from the far infrared. The conifold is briefly introduced and strings on
the conifold (the Klebanov-Witten model) are discussed. Next, fractional branes
are introduced. The duality cascade is then constructed in field theory and in
its dual supergravity description. Among the newly published results: it is
shown why supergravity sees the cascade as smooth; how the two holomorphic
couplings (dilaton and integrated two-form in supergravity) are related to the
three physical couplings in the gauge theory; that there are actually twice as
many approximate fixed points in the cascade as might be naively expected.
These notes are based on lectures given at TASI 2003 and at the 2003 PIMS
Summer School on Strings, Gravity & Cosmology.
