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Understanding the fluid flow induced by microswimmers is paramount to revealing how they interact with each other and their environment. Here, we present a three-dimensional (3D) measurement and characterization of the flow field induced by motile planktonic algal cells, Chlamydomonas reinhardtii. A single alga is captured and held stationary by a micropipette, which beats its flagella in a characteristic breastroke pattern. We track the 3D flow field around the alga by employing fast holographic imaging on 1 um tracer particles, which leads to a nominal spatial resolution of ~ 54 nm along the optical axis and ~ 44 nm in the imaging plane. The method allows us to image the flow around a single alga continuously over thousands of flagellar beat cycles and show time-averaged and phase-binned 3D flow fields. We analyze these 3D flow fields and determine the dominant force modes of the flagellar motion of C. reinhardtii. Our study demonstrates the power of holography in imaging detailed microscopic flows and provides crucial information for understanding the detailed locomotion of swimming microorganisms.