TITLE: Reference: Learning noncommutative geometry and C^* algebras
QUESTION [21 upvotes]: I am starting to study noncommutative geometry and ${\rm C}^*$ algebras so my question is:
Does anyone know a good reference on this subject?
I would like a basic book with intuitions for definitions and this kind of things. I come from algebraic geometry, so if the book talks a bit about the relation with algebraic geometry, that would be highly appreciated.
I have already taken a look at Connes's book but I find it too hard, and I'm currently studying Landi's but it lacks lots of proofs (he refers to several papers).
Thanks in advance.

REPLY [4 votes]: Let me add some new-ish books to the mix that I liked and deal with some  topics in $C^*$-algebras that have picked up some steam in recent years:
If you want an introduction to the state of the art in the theory of $C^*$-algebras then the book $C^*$-algebras and Finite-Dimensional Approximations by Brown and Ozawa is what you want to read. If you always wanted to know what completely positive maps are and how they are used to define nuclearity or if you want to remind yourself about the intricacies of tensor products of $C^*$-algebras, if you want to know everything about group $C^*$-algebras and exactness or if you work in von Neumann algebras and want to see if any of the things you do still work in the $C^*$-algebra case, it is all in this book! Apart from that it contains a lot of humorous footnotes and is a great read. Gosh, I sound like a car salesman, but I am a huge fan of this book.
Next up is Classification of Nuclear $C^*$-algebras. Entropy in Operator Algebras by Rørdam and Størmer. This is a book about more advanced topics, but if you are looking for everything related to the classification program of nuclear, simple $C^*$-algebras, which has had some recent breakthroughs, then this is your book. It gives a good description of the purely infinite case for example, so if you always wanted to read up on what makes the Cuntz algebras $\mathcal{O}_2$ and $\mathcal{O}_{\infty}$ so special, then give it a shot. The reason why I am neglecting the entropy part in this description is entirely due to my own laziness: It is still on my reading list.
If you want to know how algebraic topology, in particular sheaf cohomology, can be used to classify continuous trace $C^*$-algebras or if you want to learn about Morita equivalences and Brauer groups, then Morita Equivalence and Continuous-Trace $C^*$-Algebras by Raeburn and Williams is the book of your choice. It contains a proof of the Imprimitivity Theorem and that stuff you always wanted to know about the whole induction and restriction business.