It's not clear exactly what your first sentence is asking for (there are a variety of surveys and books). For instance, are you only interested in finite Coxeter groups?
The embeddings of the noncrystallographic Coxeter groups $H_3, H_4$ indicated in the follow-up question probably originate in older work of Coxeter and du Val (though I don't recall the exact source). These embeddings have been studied over the years in different styles, but a single comprehensive reference may not exist. One direction is indicated in a series of papers by Matthew Dyer, e.g., Embeddings of root systems. I. Root systems over commutative rings, J. Algebra 321 (2009), no. 11, 3226–3248.
Another direction of research connects the embeddings with mathematical physics, sometimes in rather a computational style, e.g., Mehmet Koca, Ramazan Koç, Muataz Al-Barwani, Noncrystallographic Coxeter group $H_4$ in $E_8$,
J. Phys. A 34 (2001), no. 50, 11201–11213.
ADDED: Older references for the embeddings were given in the notes to Section 2.13 in my 1990 book Reflection Groups and Coxeter Groups, though in the published version I wrote $D_3$ where $D_6$ is intended (this and other corrections have been maintained on my homepage).