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This book describes the development of new methods for the fabrication of monolayers and heterostructures of the transition-metal dichalcogenide TiSe2, and the subsequent investigation of the much-debated charge-density wave state in the material using angle-resolved photoelectron spectroscopy. The underlying question is whether TiSe2 is a rare example of an excitonic insulator, an exotic state of matter in which the formation of excitons causes a reconstruction of the electronic structure, accompanied by a periodic lattice distortion. Alternatively, a more conventional mechanism based on the interplay of the lattice distortion and electronic band hybridisation may be responsible for the observed charge-density wave. This question is tackled in the thesis by integrating large-area high-quality monolayers of TiSe2 in functional heterostructures with semimetallic graphite and insulating boron nitride substrates. Depending on the chosen substrate, excitonic interactions can either be allowed or strongly suppressed. The comparison of the electronic structure and the charge-density wave transition in both cases clarifies the relevance of excitons for the charge-density wave in the system. Further insights are obtained from time-resolved electronic structure measurements of the TiSe2/graphite heterostructure which reveal complex dynamics involving interlayer charge transfer and charge-density wave suppression. Finally, a prototype electrical transport device based on a single layer of TiSe2 is fabricated, demonstrating the vast opportunities for future research on epitaxial two-dimensional materials enabled by the fabrication advances developed throughout the thesis.