Badis Ydri, currently a Professor of theoretical particle physics, teaching at the Institute of Physics, Badji Mokhtar  Annaba University, Algeria, received his PhD (2001) from Syracuse University, NY, USA, and his Habilitation (2011) from Annaba University, Algeria. He is also a research associate at the Dublin Institute for Advanced Studies, Ireland, and a regular ICTP associate at the Abdus Salam Center for Theoretical Physics, Trieste, Italy. His post-doctoral experience comprises a Marie Curie fellowship (2006-2008) at Humboldt University Berlin, Germany, and a Hamilton fellowship (2001-2005) at the Dublin Institute for Advanced Studies, Ireland.Research directions: Renormalization group equation and Monte Carlo method for matrix and non-commutative field theories. Emergent physics (gauge, matter, gravity, time, etc.) and emergent geometry from matrix models. Cosmological Yang-Mills models. AdS/CFT and Yang-Mills matrix models.Other interests include stringtheory, causal dynamical triangulation, Horava-Lifshitz gravity, and supersymmetric gauge theory in four dimensions.His hobbies are reading philosophic works and history of science.

“The book collects almost all that has been achieved on the topic within the recent years, including all major results of many authors. As such, it is a nice reference work for graduate students and beginning researchers who want to pursue research in this area. Having all the results and different approaches collected in one place, together with the exhaustive list of references make this a valuable compendium to everyone working on noncommutative models of quantum field theory.” (Andrzej Sitarz, zbMATH 1371.81013, 2017)

• Preface.- Introductory Remarks.- The Non-Commutative Moyal-Weyl Spaces Rd.- The Fuzzy Sphere.- Quantum Non-Commutative Phi-Four.- The Multitrace Approach.- Non-Commutative Gauge Theory.- Appendix A - The Landau States.- Appendix B - The Traces TrtAtB and TrtAtBtCtD.- Index.

Badis Ydri, currently a Professor of theoretical particle physics, teaching at the Institute of Physics, Badji Mokhtar  Annaba University, Algeria, received his PhD (2001) from Syracuse University, NY, USA, and his Habilitation (2011) from Annaba University, Algeria. He is also a research associate at the Dublin Institute for Advanced Studies, Ireland, and a regular ICTP associate at the Abdus Salam Center for Theoretical Physics, Trieste, Italy. His post-doctoral experience comprises a Marie Curie fellowship (2006-2008) at Humboldt University Berlin, Germany, and a Hamilton fellowship (2001-2005) at the Dublin Institute for Advanced Studies, Ireland.Research directions: Renormalization group equation and Monte Carlo method for matrix and non-commutative field theories. Emergent physics (gauge, matter, gravity, time, etc.) and emergent geometry from matrix models. Cosmological Yang-Mills models. AdS/CFT and Yang-Mills matrix models.Other interests include stringtheory, causal dynamical triangulation, Horava-Lifshitz gravity, and supersymmetric gauge theory in four dimensions.His hobbies are reading philosophic works and history of science.

“The book collects almost all that has been achieved on the topic within the recent years, including all major results of many authors. As such, it is a nice reference work for graduate students and beginning researchers who want to pursue research in this area. Having all the results and different approaches collected in one place, together with the exhaustive list of references make this a valuable compendium to everyone working on noncommutative models of quantum field theory.” (Andrzej Sitarz, zbMATH 1371.81013, 2017)

• Preface.- Introductory Remarks.- The Non-Commutative Moyal-Weyl Spaces Rd.- The Fuzzy Sphere.- Quantum Non-Commutative Phi-Four.- The Multitrace Approach.- Non-Commutative Gauge Theory.- Appendix A - The Landau States.- Appendix B - The Traces TrtAtB and TrtAtBtCtD.- Index.

Badis Ydri, currently a Professor of theoretical particle physics, teaching at the Institute of Physics, Badji Mokhtar  Annaba University, Algeria, received his PhD (2001) from Syracuse University, NY, USA, and his Habilitation (2011) from Annaba University, Algeria. He is also a research associate at the Dublin Institute for Advanced Studies, Ireland, and a regular ICTP associate at the Abdus Salam Center for Theoretical Physics, Trieste, Italy. His post-doctoral experience comprises a Marie Curie fellowship (2006-2008) at Humboldt University Berlin, Germany, and a Hamilton fellowship (2001-2005) at the Dublin Institute for Advanced Studies, Ireland.Research directions: Renormalization group equation and Monte Carlo method for matrix and non-commutative field theories. Emergent physics (gauge, matter, gravity, time, etc.) and emergent geometry from matrix models. Cosmological Yang-Mills models. AdS/CFT and Yang-Mills matrix models.Other interests include stringtheory, causal dynamical triangulation, Horava-Lifshitz gravity, and supersymmetric gauge theory in four dimensions.His hobbies are reading philosophic works and history of science.

“The book collects almost all that has been achieved on the topic within the recent years, including all major results of many authors. As such, it is a nice reference work for graduate students and beginning researchers who want to pursue research in this area. Having all the results and different approaches collected in one place, together with the exhaustive list of references make this a valuable compendium to everyone working on noncommutative models of quantum field theory.” (Andrzej Sitarz, zbMATH 1371.81013, 2017)

• Preface.- Introductory Remarks.- The Non-Commutative Moyal-Weyl Spaces Rd.- The Fuzzy Sphere.- Quantum Non-Commutative Phi-Four.- The Multitrace Approach.- Non-Commutative Gauge Theory.- Appendix A - The Landau States.- Appendix B - The Traces TrtAtB and TrtAtBtCtD.- Index.