I'm not quite sure if my question belongs to this section or not, so I hope I would be posting it in the right place. Anyway, I have troubles understanding Rudin's principals of mathematical analysis. To me, everything he says, is absurd. I can't understand what he says, neither do I want to understand what he says I may say. You know, when I study mathematics, I like to have an intuition of what we're talking about before we go into technical details and abstraction. To me, a neat mathematical idea, is formed when you have gained a correct intuition and insight into the material and only after that you could care about rigor. In Rudin, he roughly explains anything. It's all theorems and definitions. It's just like he has gathered a bunch of proofs of some easy theorems proved in the hardest way and have called that a book. For example in Chapter 6, when he talks about Riemann-Stieljes integrals he assumes α (the integrator) is an increasing function. While in Apostol's analysis, Apostol doesn't require the integrator function to be increasing. So in my opinion, even though I don't know much about the subject, Rudin is just putting an unnecessary extra condition on the integrator and not only it doesn't make proofs easier, but it makes them quite tedious and hard. To cut the ranting short, I'm looking for a book that discusses mathematical analysis in a nice and understandable way. Not like Rudin that explains the simplest stuff in the ridiculously hardest way. I should add that my main area of interest, as for now, is abstract algebra. But my ultimate goal is to be a geometer that understands concepts like manifolds and other structures that are related to our understanding of the universe around us. So I'm sure I'll need to know analysis fairly well if I want to understand smooth mappings and other analytical concepts later in differential geometry and elsewhere. Having said that, please take into account that I don't have so much time to spend on an analysis book now because my university courses are really exhausting (I'm taking Calculus III, an introduction to module-theory, numerical analysis I, analysis II, topology and ordinary differential equations this semester, so I'm pretty busy with other subjects and I can't devote all my time to analysis :( ). Any helps would be appreciated. And I'm sorry If I've posted my question in the wrong place.