"...A milestone for mathematics. Connes has created a theory that embraces most aspects of 'classical' mathematics and sets us out on a long and exciting voyage into the world of noncommutative mathematics. "The book contains a colourful account of the meaning of the term 'non-commutative space,' based on an extraordinary wealth of examples, including the set of all Penrose tilings, the space of leaves of a foliation, the quantum Hall effect and an intriguing non-commutative model of four-dimensional space-time that reproduces the standard model of elementary particles from quite general considerations... "The reader of the book should not expect proofs of theorems. This is much more a tapestry of beautiful mathematics and physics which contains material to intrigue readers with any mathematical background. At the same time there is a comprehensive bibliography that will lead the reader straight to the sources and proofs of the results."
VAUGHAN F.R. JONES, University of California, Berkeley "This beautiful, ambitious, and erudite book explains, through many examples, the phenomena, tools, and some of the applications of noncommutative geometry...The book is written in a way that anyone can get some of the feeling and ideas of the subject...Connes has accomplished the wonderful feat of explaining in a simple and coherent way 20 years (or so) of his impressive work. I recommend this book most highly."
Jonathan Block, THE MATHEMATICAL INTELLIGENCER, Vol. 20, No. 1, 1998