Clinical and preclinical X-ray computed tomography (CT) provides three-dimensional anatomic imaging at high spatial and temporal resolution. However, quantitative molecular imaging is not possible in conventional CT due to similarity in the overall X-ray attenuation across the polychromatic X‑ray photon energy spectrum and the use of energy integrating detectors. However, recent developments in photon-counting detectors have led to the development of prototype photon-counting spectral CT systems that can acquire images at multiple energy levels which, when used in conjunction with material decomposition algorithms, can identify and quantify contrast agent and tissue compositions. Thus, photon-counting spectral CT can provide simultaneous anatomic and quantitative molecular imaging. However, the development of these capabilities and their application remains nascent due to a limited availability of imaging systems. Therefore, the overall objective of this dissertation was to investigate quantitative material decomposition of multiple, discrete or spatially coincident, contrast agent and tissue compositions using a prototype preclinical photon-counting spectral CT system.  Methods were developed for material decomposition using constrained maximum likelihood estimation (MLE) in the imaging domain and calibrated using multiple linear regression models of known material concentrations. The median root mean squared error (RMSE) for material decomposition of a single gadolinium contrast agent was as low as ~1.5 mM (~0.24 mg/mL gadolinium), similar in magnitude to that measured by optical spectroscopy. Material decomposition of multiple discrete contrast agent and tissue compositions was subsequently demonstrated in several models. Multiple discrete contrast agent compositions were able to be simultaneously evaluated with quantitative accuracy (RMSE) that was comparable to results for a single contrast agent and were able to be identified even against highly attenuating bone tissue. Image-based material decomposition was also able to identify contrast agents within murine models at an image acquisition time suitable for in vivo preclinical imaging. Multiple mixed, or spatially coincident, contrast agent (gadolinium and iodine) and tissue (calcium and water) compositions were identified and quantified with high accuracy (area under the receiver operating characteristic curve (AUC) > 0.8, RMSE < 12%). Finally, the methods used for mixed component material decomposition were further developed to allow elemental decomposition of Ca, P and O, which enabled discrimination of pathologically-relevant microcalcifications (hydroxyapatite versus calcium oxalate, AUC > 0.8) at a clinically-relevant size (maximum dimension < 1 mm). Thus, photon-counting spectral CT enabled quantitative molecular imaging of multiple, spatially coincident contrast agent and tissue compositions, which is not possible with current clinical molecular imaging modalities