These are the references I have used to understand the theory of lattice dynamics
Introduction to the Theory of Lattice Dynamics by M.T. Dove
Introduction to Lattice Dynamics, M.T. Dove
Dynamical Theory of Crystal Lattices, Max Born and Kun Huang
http://www.phys.lsu.edu/~jarrell/COURSES/SOLID_STATE/Chap4/chap4.pdf
PhonTS
phonopy
Giannozzi, Introduction to Calculation of Phonons and Vibrational Spectra. here