Analysis is a large branch of mathematics, and the fundamental divisions of analysis including Fourier, Real, Complex, Functional, Harmonic, are the most central parts for beginners.
[Lecture notes]Analysis and Partial Differential Equations, by Sadosky Cora
[Book]Problems in Real Analysis, by Charalambos D. Aiprantis
[Book]Classical Fourier Analysis, by S. Axler & K.A. Ribet
[Book]A Hilbert Space Problem Book, by Paul R.Halmos
[Book]Complex Analysis, by Serge Lang
[Book]Harmonic Analysis on Semigroups, by Christian Berg and Jens Peter Reus Christensen and Paul Ressel
[Book]Harmonic Analysis, by E.M Stein