Here, I'm throwing together a mix of books that I think are the best in my research areas, along with some of my all-time favorite non-math reads. This is totally my personal list, and if you've got different faves, feel free to disagree with me. Drop me an email if you have any cool book recommendations! :)
Quaternion Algebras - John Voight
Sphere Packings, Lattices and Groups - J. H. Conway and N. J. A. Sloane
Lattice Coding for Signal and Networks - Ram Zamir
Maximal Orders - Irving Reiner
Lattices Applied to Coding for Reliable and Secure Communications - Sueli I.R. Costa, Frédérique Oggier, et al.
On quaternions and Octonions: their geometry, arithmetic and symmetry - J. H. Conway and D. A. Smith
Precoding and Signal Shaping for Digital Transmission - Robert F. H. Fisher
A Classical Introduction to Modern Number Theory - Kenneth Ireland and Michael Rosen
Elementary Number Theory, Group Theory and Ramanujan Graphs - Guiliana Davidoff, Peter Sarnak and Alain Valette
Algebraic Number Thery - Frazer Jarvis
Introduction to Noncommutative Algebra - Matej Bresar
Teoria dos números algébricos - Otto Endler (Portuguese)
Introdução à Teoria dos números - José Plínio de Oliveira Santos (Portuguese)
A Máquina de Fazer Espanhoís - Valter Hugo Mãe
Ensaio sobre a Cegueira - José Saramago
O Homem Duplicado - José Saramago
As Intermitências da Morte - José Saramago
Objecto Quase - José Saramago
A viagem do Elefante - José Saramago
Brejo das Almas - Carlos Drummond de Andrade
A Rosa do Povo - Carlos Drummond de Andrade
Estorvo - Chico Buarque
A paixão Segundo G. H. - Clarice Lispector
A hora da Estrela - Clarice Lispector
Harry Potter e a Pedra Filosofal - J. K. Rowlling
Os crimes ABC - Agatha Christie
Os cinco porquinhos - Agatha Christie
Assassinato no Expresso Oriente - Agatha Christie
A Insustentável Leveza do Ser - Milan Kundera
A Harmonia do Mundo - Marcelo Gleiser