I've bought some books and I guess they're written in a way that presumes a previous background or assignment in some mathematics course - these books just spit the content directly in your face. This kind of book is not suited for me (for a first reading in the subject): I'm not in a maths course, and they wouldn't be even if I were in a maths course because I like to learn the content, It's history and why study it. I've found one book on this class and I'd like to mention it as an example:
- A book of abstract algebra, Charles Pinter;
The chapter titled Why abstract algebra? is very useful, it contains a light historical background and also some motivation for it. After this chapter the book starts to provide a normal introductory abstract algebra course.
I am looking specifically for books with this spirit, there are a lot of history books about specific fields of mathematics, for example:
- A history of abstract algebra, Kleiner;
- Number theory and its history, Oystein Ore.
They are nice books and they can provide some motivation for study, but my impression is that they are more a history book than a textbook that could be used in a undergraduate course of mathematics. You can suggest books in any mathematical subject you wish, but they have to attain to that criteria.
There's always Lawvere & Schanuel's "Conceptual Mathematics", which is an introduction to category theory aimed at undergraduates. It very much takes the approach of starting simple and motivating each next step.
To a lesser degree, Goldblatt's "Topoi" also attempts to motivate many of the ideas of topos theory, but he does so a bit more rapidly than the book above. This one is less for undergraduates, but is approachable with some determination. I can say I found the author's motivating comments helpful enough to make the material approachable at a time I had no more than a vague knowledge of set theory, so that's something.