1 Number Theory Meets Wireless Communications: an introduction for dummies like us.- 2 Characterizing the Performance of Wireless Communication Architectures via Basic Diophantine Approximation Bounds.- 3 On Fast-Decodable Algebraic Space-Time Codes.- 4 Random Algebraic Lattices and Codes for Wireless Communications.- 5 Algebraic Lattice Codes for Linear Fading Channels.- 6 Multilevel Lattices for Compute-and-Forward and Lattice Network Coding.- 7 Nested Linear/Lattice Codes Revisited