Alternative undergraduate analysis texts Other than the standard baby Rudin, Spivak, and Stein-Shakarchi, are there other alternative and comprehensive analysis texts at the undergraduate level? For example something that has general results that would serve as a very good reference book for specialist analysts in any field, whether functional, complex and measure theorists. Like change of limits, convergence of series etc.
I notice the question on undergraduate textbooks has few responses regarding analysis books of this sort.
 A: Also Abbott's Understanding Analysis.
A: I learned real analysis from Strichartz' wonderfully titled book, The Way of Analysis.  It is very wordy, but I really liked it.  I suspect that I would like it less as an instructor, simply because in preparing a lecture I don't need all the discussion, I just want to remember the main point.  But for a student, the discussion in this book can be quite beneficial, and of course as instructor, one can always keep a copy of Rudin close by.
A: V. A. Zorich's Mathematical Analysis I and II (Springer). It covers undergraduate material from an advanced viewpoint, contains lots of good physically oriented examples, and is quite comprehensive. 
A: The Student Mathematical Library has three volumes of analysis problems for undergraduates:


*

*Real Numbers Sequences and Series

*Contintuity and Differentiation

*Integration
The best part of analysis at this level is how it enhances calculus.   
A: I really enjoyed Jean Dieudonne's first volume.
A: Karl Stromberg
Introduction to Classical Real Analysis (Wadsworth & Brooks/Cole Mathematics Series)
A: Roger Godement Analysis(I-IV-in french,I-II-in english)contains more than Bourbaki's "Functions of one real variable",has motivation and historical insight(not quite a textbook however..)
A: Zygmund and Wheeden's Measure and Integral is quite nice, and compact.  We used in at the University of Alberta for our 4th year analysis sequence (a full year course).  It does assume the students coming into the course are fairly mature in how they think about mathematical formalism.  Probably not the right textbook for a group of students coming out of a purely "service" calculus sequence. 
On the other end, Hubbard's Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach is sort of like a souped-up service-calculus course that's bordering on being analysis.  You don't go so far as measure theory, but you do calculus so well some people might consider it to be a baby analysis course. 
A: Amann, Analysis I, II, III
Both original German version, and English translation.
It contains most important things 'all-in-one', really comfortable to read. 
A: The recently released book Real and Complex Analysis, by Apelian and Surace, covers basic real and complex analysis together at an undergraduate level. 
A: Knapp's "Basic Real Analysis" covers a lot of material and takes care with some of the topics you mentioned. I'm not completely sure if I would have wanted it as my very first analysis book but it would have been good to have at hand and I think it would be a good text to work through.
A: We used Real Analysis by N.L. Carothers when I took my first course on metric spaces quite some years ago. Its only weakness is that it doesn't have any material on Hilbert spaces (at least if I recall correctly) and that you probably need the students to have learned of real sequences, real continuous functions and the Riemann/Darboux integral in an earlier course.
Link: Amazon, Google Books.
A: I find this question strange because Stein-Shakarachi series covers different things compared to baby Rudin. Anyway if you are looking for some notes that cover basic analysis, here is one. It covers from basic calculus up to multivariable integration (Jordan content), and along the way introduced topology on $\mathbb{R}^n$ and differential forms on $\mathbb{R}^n$. Originally there was also a brief introduction to measure theory (up to Radon-Nikodym), but it seems that this part was put in another file. 
Edit: Link replaced.
A: The first analysis course I ever took used the book "Elementary Analysis" by Ross. It's basically baby-baby-Rudin. Ross's book (if you include the exercises and the optional sections) covers more or less the same material as the first 8 chapters of baby-Rudin, but the exposition is much friendlier and it's more easy-going for a beginner. When I say "beginner" here I really mean beginner -- someone who has never even written a rigorous mathematical proof. The book would probably be very boring and tedious for someone above this level.
A: Gaughan's book and the book by Swartz and Depree are excellent for undergraduate Analysis. Swartz Depree also does the Gauge integral.
A: I'm surprised no one has said Marsden and Hoffman's "Elementary Classical Analysis", but perhaps it is too elementary or classical. I didn't learn from it as an undergrad, but I did find myself turning to it as I worked problems from "Berkeley's Problems in Mathematics" by de Souza and Silva. M&H fleshes out a lot more detail, which Rudin spares for the sake of elegance or relegates to the exercises. I wish I had it or Korner's book "A First Second or Second First Course in Analysis" alongside Rudin when I first studied analysis. In particular, I prefer Marsden and Hoffman's treatment of Arzela-Ascoli over Rudin's.
A: There's Yeh's Theory of Measure and Integration which covers almost everything Folland does, but in a (really) verbose fashion.
A: Terence Tao has published his notes for undergrad analysis as a book: 
http://terrytao.wordpress.com/books/
The original notes can be found on his webpage. I'm not sure exactly what the differences between the notes and the book are.
A: Charles Pugh's Real Mathematical Analysis covers a wide range, starting from real numbers, topology, and basic 1D calculus, and then moving into multivariable calculus, function spaces, and Lebesgue measure/integration, all in a compact 450 pages. The writing is clear and quirky, and there are lots of interesting and hard problems.
A: Nobody has mentioned Folland's "Real Analysis with Applications"??  This was the textbook for my undergraduate real analysis course (measure theory, Banach spaces, Hilbert spaces), and I still go back to it all the time.  I am not yet all that experienced (I just finished my third year of graduate school), but overall I have gotten more use out of this book than any other that I own.
It has the most comprehensive swath of applications of analysis of any introductory text I have ever encountered: basic functional analysis, Fourier theory, probability theory, distributions, Hausdorff measures, Haar measure, smooth measures, and more.  The early material is covered with all the appropriate detail, while the later material quickly provides the essential definitions and results needed to come to grips with an unfamiliar idea in the literature.  Also, the exercises are abundant and uniformly fantastic.  My only complaints are that some of the later proofs are hard to read, and there is sadly no discussion of the spectral theorem.
A: I liked Kolmogorov & Fomin's books when I was an undergrad.  Not much complex analysis in them, but they're great if you like functional analysis.  
A: How about the Apostol's books?
A: T.W. Korner has a book. On the off-the-beaten-track side, you can always use Keisler. Finally, for some good-old dialectic materialism and entertainment value you can use G.M. Fichtenholz (couldn't find a link to that - but they still used a Hebrew translation (well - more or less) in Israel not so long ago).
A: Shilov's Elementary Real and Complex Analysis is comprehensive, straightforward, and as a Dover book, is excellently priced.
A: A very alternative approach is Carol Schumacher's Closer and Closer: Introducing Real Analysis which uses inquiry-based learning / the Moore method.  (http://www.jblearning.com/catalog/9780763735937/)
A: I learnt measure theory and some other analysis from Royden: "Real Analysis".  That was quite interesting!
A: There's a period of time when I'm trying to substitue the whole undergraduate real analysis course with the alternative choice:
Use a general topology book like Klaus Janich's Topology and a decent measure theory book like Cohn's Measure Theory.
The material I mentioned above can be a ponderable substitution of a real analysis course if you really hate the classics so much...
A: A really great new book out is "Real Analysis for the Undergraduate - With an Invitation to Functional Analysis" by Matthew Pons.  This book offers a classical treatment of undergraduate analysis, but then offers a nice introduction to measure theory and integration theory.  Also, at the end of each chapter there are really nice glimpses into ideas from functional analysis and operator theory.
A: I just took my first analysis course and used "Fundamental Ideas of Analysis" by Michael Reed and enjoyed it very much.  Good motivating points, good problems, and has allowed me to access other, more deep, analysis texts.
link: Amazon
