Duistermaat and Kolk's multidimensional real analysis. Perhaps the theory portion isn't the greatest, but that selection of exercises is. Half the book consists of just problem statements from all kinds of different domains, like physics, the Riemann zeta function, complex analysis, differential geometry. Even browsing through the different problems is amazing.
Bloch's the real numbers and real analysis. This is an introductory real analysis text, but what makes it stand out is its careful focus on foundations. It starts by giving the Peano axioms, and rigorously constructing Z, Q and R in a way no other book does (although Tao kind of gives the idea, but imo doesn't work it out much). The book then continues by rigorously going over the properties of the real numbers, including a proof that decimal expansions of the real numbers exist and are "unique". Then it continues to usual analysis topics, but even there there is a focus towards the foundations, for example he proves that the intermediate value theorem is equivalent to completeness of the real numbers, and there are many other neat bits like this.
Carothers, real analysis. I just really love how this book does real analysis. He assumes you are familiar with real analysis on R and a tiny bit of linear algebra (vector spaces and linear maps, nothing more). Then he goes on doing metric spaces, function space and measure theory on R. There are a ton of problems which really help a lot in internalizing the theory.
Freitag & Busam's complex analysis. Here are two books on complex analysis that I really like. Great collection of problems (most of which are solved in the back or with hints!), and nice theoretical development.
Anderson & Feil, abstract algebra. Not too different from a standard AA text, but does rings first and only then groups. I always felt this to be better since for example quotient rings are more intuitive to grasp than quotient groups.
Brannan's geometry: Does geometry from the point of view of Klein: covers affine and projective geometry (and motivates it), and hyperbolic, elliptic and inversive geometry and relates them to eachother using the language of group theory. The problem selection isn't the greatest though.
Any book by Keith Kendig, especially his book on plane algebraic curve. He throws rigor out of the window so it's not meant as a standard textbook, but he does offer a damn lot of intuition and nice pictures!
Cox, O'shea and Little's "ideals, varieties and algorithms" is in my opinion the best introduction to algebraic geometry. There is a heavy focus towards algorithms (for example Grobner bases) though. But he really gives intuition to why we should care about algebraic geometry and why some questions arise naturally.
Silverman's "Friendly introduction to number theory". Like all of Silverman's books this is a gem.
Not sure if it's obscure, but I really like Simon's comprehensive course in analysis, and Harthorne's "Euclid and beyond" too.
