Understanding the locomotion of microorganisms is essential for insights into microbial ecology, infection, and colonization processes. Although two-dimensional microscopy has been widely used to study microswimmer motility, it does not capture the full extent of their three-dimensional (3D) movement. Recent advances in defocused particle tracking, holographic tracking velocimetry, and stereo-microscopy face challenges in achieving high resolution at larger particle densities and tracking multiple microswimmers in suspension. In this work, we introduce a novel multi-camera microscopy system that significantly improves the accuracy of 3D microswimmer tracking. Our system uses four sCMOS cameras to image microorganisms within a 2.5 × 2.5 × 2 mm3. We assess the performance of our microscopy system by tracking a population of the unicellular motile algae Chlamydomonas reinhardtii. An in-house tracking algorithm based on the projective geometry framework enables tracking with reprojection errors below 0.3 body lengths. This system supports imaging and tracking particle source densities of 0.32, higher than other existing single camera 3D microscopy techniques. Analysis of C. reinhardtii trajectories in 3D reveals a predominance of left-handed chirality and helical swimming patterns. Moreover, our 3D tracking data provide translational and rotational diffusion coefficients that differ from those obtained using traditional two-dimensional methods.