Noncommutative Spaces and Algebras of Functions.- Projective Systems of Noncommutative Lattices.- Modules as Bundles.- A Few Elements of K-Theory.- The Spectral Calculus.- Noncommutative Differential Forms.- Connections on Modules.- Field Theories on Modules.- Gravity Models.- Quantum Mechanical Models on Noncommutative Lattices.

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An Introduction to Noncommutative Spaces and Their Geometries

On the classification of inductive limits of sequences of semisimple finite-dimensional algebras

These lectures notes are an intoduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate applications to Yang-Mills, fermionic and gravity models, notably we describe the spectral action recently introduced by Chamseddine and Connes. We also present an introduction to recent work on noncommutative lattices. The latter have been used to construct topologically nontrivial quantum mechanical and field theory models, in particular alternative models of lattice gauge theory. 
Here is the list of sections: 
1. Introduction. 2. Noncommutative Spaces and Algebras of Functions. 3. Noncommutative Lattices. 4. Modules as Bundles. 5. The Spectral Calculus. 6. Noncommutative Differential Forms. 7. Connections on Modules. 8. Field Theories on Modules. 9. Gravity Models. 10. Quantum Mechanical Models on Noncommutative Lattices. 
Appendices: Basic Notions of Topology. The Gel'fand-Naimark-Segal Construction. Hilbert Modules. Strong Morita Equivalence. Partially Ordered Sets. Pseudodifferential Operators

An Introduction to Noncommutative Spaces and their Geometry

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Entropy for automorphisms of II1 von neumann algebras

Equivalence and traces on C∗-algebras

C∗-algebras with a two-point dual

Lectures on Operator Algebras

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Automorphisms of crossed products

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Horst Behncke

Papers

C∗-algebras with a two-point dual

Lectures on Operator Algebras

Automorphisms of crossed products

Generators of $W^{^*}$-algebras

C∗-algebren mit geordneten ideal folge