There are four books in the Princeton Lectures in Analysis series:
Book I. Fourier series and integrals.
Book II. Complex analysis.
Book III. Measure theory, Lebesgue integration, and Hilbert spaces.
Book IV. A selection of further topics, including functional analysis, distributions, and elements of probability theory.

I’m currently reading Book II, for ACM101, which assumes you’re already familiar with complex analysis. This is a great book– I read the first three chapters in about two and a half hours (just skimming the first, on basic facts in analysis and terminology). So, I’ve already seen the big three topics: contour integration (Goursat/Cauchy’s theorems), regularity, analytic continuation. I wish I’d picked this book up before.

Maybe I’ll read the other three, if they’re as good as this one. That would be a good way to review all the stuff I should already know.

Possibly relevant posts:

• Convergence (2/7/2005)
• Real Analysis and Fourier theory (3/4/2005)
• El Fin (9/28/2007)