"Elementary Real Analysis" is written in a rigorous, yet reader friendly style with motivational and historical material that emphasizes the " big picture" and makes proofs seem natural rather than mysterious. Introduces key concepts such as point set theory, uniform continuity of functions and uniform convergence of sequences of functions. Covers metric spaces. Ideal for readers interested in mathematics, particularly in advanced calculus and real analysis.
Damn good! Probably one of the best intros to real analysis (sans measure theory and Lebesgue integration). Starts off more leisurely than say baby Rudin (Principles of Mathematical Analysis), but still covers a lot of ground with all the 'enrichment' and 'advanced' topics. Exercises galore, many with hints.
Prepares you well for the authors' (measure-theoretic) "Real Analysis".