Manually segmenting multiple sclerosis (MS) cortical lesions (CLs) is extremely time consuming, and past studies have shown only moderate inter-rater reliability. To accelerate this task, we developed a deep-learning-based framework (CLAIMS: Cortical Lesion AI-Based Assessment in Multiple Sclerosis) for the automated detection and classification of MS CLs with 7 T MRI. Two 7 T datasets, acquired at different sites, were considered. The first consisted of 60 scans that include 0.5 mm isotropic MP2RAGE acquired four times (MP2RAGE×4), 0.7 mm MP2RAGE, 0.5 mm T ₂ *-weighted GRE, and 0.5 mm T ₂ *-weighted EPI. The second dataset consisted of 20 scans including only 0.75 × 0.75 × 0.9 mm ³ MP2RAGE. CLAIMS was first evaluated using sixfold cross-validation with single and multi-contrast 0.5 mm MRI input. Second, the performance of the model was tested on 0.7 mm MP2RAGE images after training with either 0.5 mm MP2RAGE×4, 0.7 mm MP2RAGE, or alternating the two. Third, its generalizability was evaluated on the second external dataset and compared with a state-of-the-art technique based on partial volume estimation and topological constraints (MSLAST). CLAIMS trained only with MP2RAGE×4 achieved results comparable to those of the multi-contrast model, reaching a CL true positive rate of 74% with a false positive rate of 30%. Detection rate was excellent for leukocortical and subpial lesions (83%, and 70%, respectively), whereas it reached 53% for intracortical lesions. The correlation between disability measures and CL count was similar for manual and CLAIMS lesion counts. Applying a domain-scanner adaptation approach and testing CLAIMS on the second dataset, the performance was superior to MSLAST when considering a minimum lesion volume of 6 μL (lesion-wise detection rate of 71% versus 48%). The proposed framework outperforms previous state-of-the-art methods for automated CL detection across scanners and protocols. In the future, CLAIMS may be useful to support clinical decisions at 7 T MRI, especially in the field of diagnosis and differential diagnosis of MS patients.