Laminar heat and mass transfer is central to a wide range of industrial processes, encompassing (thermal) processing of viscous fluids, compact equipment for process intensification and emerging micro-fluidic devices. Many of these applications incorporate the "static-mixing principle" (stirring of a throughflow by internal elements) for mixing and heat-transfer enhancement. Investigations on static mixers primarily concern numerical simulations. Experimental studies, on the other hand, are relatively rare and to date restricted to visualization of mixing patterns or integral quantities as e.g. pressure drop and heat-transfer coefficients. The present study expands on this by quantitative experimental analysis of three-dimensional (3D) flow fields and streamline patterns in a representative static mixer using 3D Particle-Tracking Velocimetry. This necessitates tackling of (internal) refractions and reflections caused by the complex mixer geometry. Comparison of experimental results with numerical predictions reveals a good agreement.