One of my favourite books for harmonic analysis is Fourier analysis by Javier Duoandikoetxea. In fact, I would recommend that as your first port of call for learning harmonic analysis if you already have some background (such as an undergraduate/postgraduate course in harmonic analysis). That is a terrific reference for background regardless of what you want to do with harmonic analysis. I would tackle this before moving onto Elias Stein's book "harmonic analysis: real-variable methods, orthogonality and oscillatory integrals" (also a great book).
As mentioned above, it really depends on what type of harmonic analysis you are interested in, but I would certainly recommend those as well as harmonic analysis by Katznelson, the two volume books by Grafakos, both of Stein's books on "introduction to Fourier analysis on Euclidean spaces" and "singular integrals and differentiability properties of functions" are useful for singular integrals. I'd also recommend a treatise on trigonometric series by Bary. Zygmund's two volume books on trigonometric series are good, but I would tackle a few other books on harmonic analysis before going for it. It is quite complex in comparison to the other references and will not help much if you do not already have a foundation in harmonic/Fourier analysis.
If you like abstract harmonic analysis, go for "principles of harmonic analysis" by Anton Deitmar.
Harmonic analysis and PDEs by Christ, Kenig and Sadosky is good for specific directions (such as PDEs, probability, curvature and spectral theory).
Terence Tao's website is great for lecture notes (all academic resources on his website are great!)
Finally, "lectures on nonlinear wave equations" by Christopher Sogge and "nonlinear dispersive equations" by Terence Tao are great books that have a focus on dispersive PDEs using techniques from harmonic analysis (such as Littlewood-Paley theory).
Just to add an extra reference, check out "Topics in Harmonic Analysis Related to the Littlewood-Paley Theory" also by Elias Stein