We've shared inspirational and interesting links to various musicians and composers of Middle-earth related music, and I'd like to introduce one of my favourites. Johan de Meij, of the Netherlands, wrote his LotR Symphony for concert band back in the 1980s. That means the music predates Howard Shore's LotR movie soundtrack by quite a few years.
It consists of five movements:
1. Gandalf
2. Lothlórien
3. Gollum
4. Journey in the Dark
5. Hobbits
I really enjoy the mood and characterization the composer has put into this music. It is open to interpretation; each movement has a different feel to it, and I find it very beautiful.
I've found several links on YouTube. This one leads from the first movement to the subsequent ones, so may provide the best introduction:
LotR Symphony
I hope you enjoy as much as I do!