TITLE: Expository texts on advanced subjects
QUESTION [8 upvotes]: I'm reading The Princeton companion to Mathematics and Basic Notions of Algebra by Shafarevich. Both of them are really pleasant reading, the first one treats the topics from a more elementary point of view and the second one use advanced examples from other areas and from algebra itself. From this I got to know the Encyclopaedia of Mathematical Sciences of Springer, I'm wondering if you know more texts like this, they don't have to be books, they could be papers/blogs/etc. I'm looking for well explained and motivated introductions to advanced fields/ideas in contemporary Mathematics.

REPLY [4 votes]: A book that comes to mind is Abhyankar's Lectures in Algebra. It is a fascinating book.
Miles Reid's Undergraduate Commutative Algebra should also fit your description. I am not sure about his other undergraduate book on Algebraic Geometry. I have not read this book.
I also like notes by Dr. David R. Wilkins. He has notes on a wide variety of subjects.
Notes by James Milne cannot be overlooked.
I don't know if Richard Courant's "What is Mathematics?" qualifies as an introduction to advanced areas in contemporary mathemtics. I certainly learned a lot from it at some point.
May be, Mumford's Red Book qualifies your criteria?
A nice introduction to Algebraic Geometry is Fulton's book "Algebraic Curves".
Ravi Vakil's notes on Foundations of Algebraic Geometry are also becoming very popular (though they are not elementary).
I also like Cox, Little and O'Shea's "Ideals, Varieties and Algorithms".
Rosen and Ireland's "A Classical Introduction to Modern Number Theory"
The Catsters on youtube explaining Category Theory.