Twisted K-theory has received much attention lately due to the work of Free-Hopkins-Teleman that relates twisted K-theory to the Verlinde Algebra. This monograph contains the thesis work of Mehdi Khorami on twisted K-theory which starts with presenting motivations and and precise definitions. There is then constructed a spectral sequence that converges to twisted K-theory of a given space X equipped with a given twist. Here a twist of X is a three-dimensional integral cohomology class. Contained in this spectral sequence are certain Tor groups. Investigation of these Tor groups shows that they have to vanish. This in fact turns out to be true which in turn results in a universal coefficient theorem for twisted K-theory. This theorem helps one to understand and compute twisted K-theory more easily.