Need help finding graduate analysis book

[jav]

I have just taken real analysis I and II (single and multivariable respectively) as an undergrad. I am planning on taking the grad analysis course next year.

From what I gather Rudin seems to be the time-tested bible of analysis, but I don't know at what level the book is written. Can anyone recommend a graduate level real analysis book?

Also, I am looking to get a head start on complex analysis, so if anyone could share the name of a good complex analysis text, I would appreciate it.

Thanks

[Landau]

Please elaborate on the course. What are the subjects treated? Analysis is a big subject. Rudin already has three textbooks (principles, real and complex, functional) on analysis.

[VeeEight]

Royden's Real Analysis is a classic and features chapters on the Real line, Metric spaces, Topological spaces, Lebesgue integration, Banach spaces, and Measure theory. It doesn't feature complex analysis, however. Complex analysis by Gamelin is a good book and covers a year long course in the subject (or more or less depending on what you know).