Strong Coulomb interactions are either suspected or known to play a prominent role in material classes such as high temperature superconductors, charge density waves, and Mott insulators among many others. These interactions are quantified by the charge density response function, chi(q,w) (or the closely related inverse dielectric function). The measurement of the energy- and momentum-resolved chi(q,w) over a large phase space of q and w, however, presents a significant experimental challenge. Traditional methods to measure chi(q,w) have suffered from either one or more major drawbacks. To address this problem, the development of a spectroscopic technique, momentum-resolved electron energy loss spectroscopy (M-EELS), was undertaken. Because many of the material classes that exhibit these unusual ground states tend to be layered or quasi-two dimensional, M-EELS presents a promising approach to measuring the energy- and momentum-resolved charge density response. Since the technique is not widely used, however, the M-EELS results obtained as part of this thesis were compared to other probes in the relevant ranges of phase space to ensure consistency. Furthermore, a theoretical framework was worked out to demonstrate explicitly the relationship between the scattering cross section and c(q,w). M-EELS experiments were conducted on a high-temperature superconductor, Bi2Sr2CaCu2O8+d, a charge density wave material, TiSe2, and a topological insulator, Bi2Se3. It was determined that the bosonic origin of quasiparticle kinks often seen in angle-resolved photoemission studies can be identified using M-EELS. Lastly, the observation of a novel electronic collective mode in TiSe2 is presented as strong evidence for an excitonic insulator phase in this compound.
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Collective excitations in layered materials with momentum-resolved electron energy loss spectroscopy