Breast density (BD), defined as the volumetric fraction of glandular tissue within the breast, is a well-established risk factor for developing breast cancer. Current methods for measuring BD are limited by subjectivity or the two-dimensional nature of conventional mammography. An accurate, low-dose, quantitative method is desirable to improve individual risk assessment and optimise screening intervals. Hyperspectral X-ray detectors, capable of capturing the full energy spectrum of incident radiation, have shown promise in material composition analysis. This thesis investigates the potential of hyperspectral X-ray detectors, specifically the HEXITEC detector, for measuring BD. The first part of this work involved characterising the HEXITEC detector in terms of spectral response and count rate capability. A Geant4-based Monte Carlo model was developed to simulate the detector’s response, used throughout this work. Algorithms to correct for fluorescence and charge-sharing effects in Bremsstrahlung spectra were developed, leading to good agreement between incident and corrected spectra. The impact of varying count rates on spectral performance was evaluated, identifying a maximum operating flux of 2.5×10⁵ photons cm^-2 s ^-1 before spectral distortions ensue, emphasising the need for faster detectors for in-vivo imaging applications. The second part of the work focused on developing a neural network-based method for calculating BD from HEXITEC spectra. Breast phantoms of varying thickness and density were created using adipose and glandular tissue equivalent slabs. At mean glandular doses (MGD) of 0.50-1.16 mGy and 1.00-2.32 mGy, the neural network predicted phantom BD with mean absolute errors (MAE) of 6.9% and 6.2% per pixel, respectively. Finally, an in-silico study utilised simulated exposures of VICTRE digital breast phantoms to train the neural network. The network predicted phantom BD with a MAE of 4.5% at MGDs of 0.09-0.39 µGy. This work establishes the feasibility of hyperspectral X-ray detectors for accurate, low-dose BD measurement.