I'm not sure if this question has been asked before. I'm interested in finding textbooks that are "like" Stephen Abbott's Understanding Analysis. The distinctive feature about this textbook is that it motivates the reasoning involved in the proofs prior to presenting the proofs, making the construction behind the proofs seem all the more reasonable.
I'm hoping if other people can list textbooks similar to Abbott's book in other fields of study, algebra, complex analysis etc. The books need not be at a level comparable to that of Abbott's books; the books can be of intermediate-advanced difficulty as well.
This is a late answer ($3$ years late!), but I thought I'd put my two cents in just in case somebody ever stumbles across this question.
One book that matches your description perfectly (and, I'd argue, is even more successful at what it does than Abbott's) is Michael Sipser's Introduction to the Theory of Computation. Instead of assuming the definition-theorem-proof structure standard in mathematical literature, Sipser splits his proofs into two parts: a "Proof Idea", which explains the motivation behind each proof and fleshes out the details, followed by the condensed Proof to provide the rigorous formalism.
Exercises are similarly segmented: each chapter is followed by an "Exercises" section, providing the student with an opportunity to practice basic computations and apply the learned definitions to some elementary results, and a "Problems" section, which compiles more challenging results. As is standard, some important theorems that the main text couldn't accommodate are relegated to the Problems section. The book is perfectly linear and the level of understanding demanded throughout is very even.
Perhaps the only piece of critism I can think of for this book is that it isn't advanced enough. But (in case of persisting interest) this is easily rectified by following it up with a more advanced text.