Phonons are the quanta of vibration of the lattice. They are vital in the description of charge and heat transport, taking part in optical absorption processes in indirect semiconductors, and making up the bosonic ''glue'' that holds superconducting states together. The concept of quantum geometry encloses the geometrical features of the electronic Hilbert space. In this Thesis, we build a theory to calculate the geometric contribution to phonon dispersions, enabling us to define, for the first time, a momentum-resolved quantifier of quantum geometry in an observable quantity (the phonon dispersion relation). The theory is then applied to graphene, a monoatomic layer of carbon atoms. The results are discussed in the light of fundamental symmetry considerations and universal laws.