Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutat

Foreword. Introduction. Projects. A Taste of Category Theory. Noncommutative Spaces. Grothendieck Categorical Representations. Sheaves and Dynamical Topology. Bibliography. Index.