This volume contains of the proceedings of the CECAM {Centre d'Etudes de Calcul Atomique et Moleculaire} workshop on "Ab Initio Calculation of Phonon Spectra" which took place at the campus of the University of Antwerpen (Universitaire Instelling Antwerpen) on June 4 and 5, 1981. This workshop was sponsored by the Universitaire Instelling Antwerpen, by the Belgian "Nationaal Fonds voor Weten- schappelijk Onderzoek" and the Belgian Ministry of Education and Cultural Affairs. Although the calculation of phonon spectra in a solid has long been known to solid state physicists, it is only in the last decade that a macroscopic theory which treats the response of the electrons to the vibrations of the ions has been developed in a successful way. In the case of semiconductors numerical calculations of phonon frequencies were not performed until very recently due to the complex- ity of the problem. The correct treatment of the electron in the crystal has also led to an investigation of electron-phonon inter- action, including many body effects. Success has been achieved in the calculation of phonon anomalies and the coupling parameters in transition metals. In the case of surfaces the conductions for the appearance of electronic instabilities and the coupling of the resulting charge density wave to the lattice have been studied.