Purpose: To develop a method for rapid sub-millimeter T1, T2, T2* and QSM mapping in a single scan using multi-contrast Learned Acquisition and Reconstruction Optimization (mcLARO). Methods: A pulse sequence was developed by interleaving inversion recovery and T2 magnetization preparations and single-echo and multi-echo gradient echo acquisitions, which sensitized k-space data to T1, T2, T2* and magnetic susceptibility. The proposed mcLARO used a deep learning framework to optimize both the multi-contrast k-space under-sampling pattern and the image reconstruction based on image feature fusion. The proposed mcLARO method with R=8 under-sampling was validated in a retrospective ablation study using fully sampled data as reference and evaluated in a prospective study using separately acquired conventionally sampled quantitative maps as reference standard. Results: The retrospective ablation study showed improved image sharpness of mcLARO compared to the baseline network without multi-contrast sampling pattern optimization or image feature fusion, and negligible bias and narrow 95% limits of agreement on regional T1, T2, T2* and QSM values were obtained by the under-sampled reconstructions compared to the fully sampled reconstruction. The prospective study showed small or negligible bias and narrow 95% limits of agreement on regional T1, T2, T2* and QSM values by mcLARO (5:39 mins) compared to reference scans (40:03 mins in total). Conclusion: mcLARO enabled fast sub-millimeter T1, T2, T2* and QSM mapping in a single scan.