It is an absolute failure of mathematics culture that a book such as this is outside the norm.<br><br>Mathematics culture seems to enjoy trying to make learning mathematics as non-intuitive and painful as possible. Mathematicians seem to take sadist pleasure in only giving trivial examples (an example of a group is the real numbers.  An example of a ring is the real numbers, and example of blah blah blah, is the real numbers.....)<br><br>Conversely, even many many graduate level physics textbooks focus on clarity, pedagogy, and understanding.  Why make things harder than they need to be?<br><br>Abbott takes the opposite approach and has produced an absolute gem of book.  I hope he has ushered in a new era of mathematics pedagogy.  One can clearly be both rigorous AND pedagogical.  It is a shame it has taken this long for a mathematician to realize this is so.<br><br>Commendable