Can you connect an Apple TV to a stereo system for music, in addition to HDMI to the TV?

You can also take an audio feed from the HDMI connection if you have an AV amp that supports it. My AV Receiver (Pioneer) is now more than 6 years old but it drives all my devices - Satellite TV Receiver / DVD Player / Apple TV / PlayStation 3, outputting to my home theatre speakers (KEF) Newer AV Amps even have Airplay support built in so you could play music straight from an iPhone or iTunes across your home Wi-Fi to your home theatre. Something like this: http://www.pioneer.eu/uk/products/42/98/405/SC-LX85/index.html

The older Apple TV models have an optical out. This will produce good sounding audio. However, the newest AppleTV only has HDMI out. This is problem for music, and also for digital audio. Many TVs downmix Dolby 5.1 to stereo.  (I am looking at you Samsung)One solution is a splitter which extracts the audio.

Yes, you can use the optical audio port to connect the Apple TV directly to a stereo receiver. New receivers will already have an optical audio port or you can buy an adaptor to convert to analog RCA cables. I use such an adaptor and it works great! Of course you still need some sort of visual interface in order to select the music to play. This can be the TV or an iOS device using the remote app.

This has already been answered well below, but here's how I do it: HDMI output of current Apple TV model goes into my receiver Receiver handles all audio decoding (including 5.1 or stereo), and has a throughput HDMI to send video (and audio if I want it, which I do not) to my TV. Thus, I can listen to audio-only (by turning on my receiver but not my TV, then streaming (pushing) the audio FROM iTunes on my phone, laptop, Mac music server, etc. TO the Apple TV. Or I can "pull" audio by turning on the TV+stereo and using AppleTV to stream audio from my Mac music server (though that means the TV is on and showing the album art, which is nice but a waste of power). Or I can stream audio from Apple Music or wherever Or I can watch AppleTV In all of these cases, the sound comes exclusively from my stereo, which is much better at handling sound than my television.Note that I could have wired this differently, by sending HDMI from AppleTV to my TV, then using either a 'through' HDMI cable or a digital audio cable (Toslink or other) to send the audio to my stereo. That would be more setup trouble than it's worth, since that would have meant my TV would likely have to be On in order to route audio. Also, my particular TV didn't happen to have these connections.So the setup can be done several ways, depending on what stereo and TV you have. Of course, if you don't have a stereo and just want audio through your TV, then the connection is simple (but in that case, you might as well replace the audio with a kazoo and a clock radio because clearly you wouldn't care how it sounds).