Introduction to Abstract Harmonic Analysis for undergraduate background I'm looking for a good starting book on the subject which only assumes standard undergraduate background.
In particular, I need to gain some confidence working with properties of Haar measures, so I can better understand the spaces $L^{p}(G)$ for a locally compact group $G$.
For some perspective on what I currently know, I can't yet solve this problem:  Verifying Convolution Identities
Something with plenty of exercises would be ideal.

Dym and McKean's book Fourier Series and Integrals is very well-written, begins with standard undergraduate harmonic analysis on $\mathbb{S}^1$ and $\mathbb{R}$, and devotes the latter half to Fourier analysis on finite groups and some good examples of compact groups ($SO(3)$ in particular).
Since I have not yet read it (it was recommended to me by my advisor, so I am in the process of acquisition), I am not sure at what level Helgason's book Topics in Harmonic Analysis on Homogeneous Spaces is written. You might consider checking it out to see if you can follow his arguments, or at least understand statements of results.
