The recently proposed, fully multi-scale theory of doublet mechanics, presented here in a self-contained form, offers unprecented opportunities to reconcile the discrete and continuum representations of solids while maintaining a simple analytical format and full compatibility with lattice dynamics and continuum mechanics. Its applications include micro-electro-mechanical systems (MEMS), granular and particulate media, nanotubes and peptide arrays. Novel results are reported, including the identification of a new class of dispersive surface waves, and the presentation of methods for the experimental determination of the essential microstructural parameters. The relationships between doublet mechanics, lattice dynamics, and continuum theories are examined.