Myocardial perfusion, the blood flow to the heart muscle, can be evaluated by tracing the passage of a contrast agent using cardiac magnetic resonance (CMR) imaging. This technique, well-established for diagnosing coronary artery disease, is limited by the necessity for breath-holding, subjective assessment, and low myocardial coverage. In this thesis, we aim to address these limitations of contrast-enhanced myocardial perfusion CMR. We developed a pulse sequence and post-processing pipeline to quantify myocardial perfusion using free-breathing 3D contrast-enhanced CMR. To restrict volume acquisition to the diastolic phase, characterized by minimal cardiac motion, we employed optimal slice oversampling, maximal partial Fourier acquisition, and cartesian undersampling in spatial and temporal domains. To mitigate the effects of breathing, respiratory tracking and image registration were performed. Collaborations for the reconstruction of raw data utilizing deep learning and image registration were established. Validation in healthy volunteers demonstrates that the developed pulse sequence enables isotropic 3D acquisition (3.6 x 3.6 x 3.6 mm^3) of an arterial input function (AIF) and myocardial signal during each cardiac cycle, up to heart rates of 76 bpm. Obtained AIF images exhibit sufficient resolution for extracting the left ventricular blood pool signal and registered myocardial images are of good quality. We investigated and validated a method to convert signal intensity to T1, which is required for MBF quantification. While T1 estimates from the AIF images approximate reference values up to 500 ms well, underestimation was observed from the myocardial images and for high T1 values.