Great project from Patrick Müller up on Hackster.io.
As a kid, I used to build AM radios but never quite managed to build FM radios. They were just too complicated. Nowadays, you can get a complete FM radio tuner on a chip but these chips are surface-mount components and difficult for a hobbyist to work with. Fortunately, Sparkfun makes a breakout for the Silicon Laboratories Si4703 FM radio tuner chip (datasheet), which breaks out all pins. I will show you how you can build a complete FM radio around this breakout and use an Arduino to control the tuner functions over the built-in two-wire control interface. Sparkfun provides a complete library making this easy to program.
At the same time, I added a cool little OLED display to the project with very high contrast and very low power consumption. Last but not least, I will show you how you can build a great-sounding mono audio amplifier from a minimum of parts. The finished radio runs on three AA-batteries for many, many hours.