Angular momentum is one of the most fundamental physical quantities governing galactic evolution. Differences in the colours, morphologies, star formation rates and gas fractions amongst galaxies of equal stellar/baryon mass M are potentially widely explained by variations in their specific stellar/baryon angular momentum j. The enormous potential of angular momentum science is only just being realised, thanks to the emergence of the first simulations of galaxies with converged spins, paralleled by a dramatic increase in kinematic observations. Such observations are still challenged by the fact that most of the stellar/baryon angular momentum resides at large radii. In fact, the radius that maximally contributes to the angular momentum of an exponential disk (3Re-4Re) is twice as large as the radius that maximally contributes to the disk mass; thus converged measurements of angular momentum require either extremely deep IFS data or, alternatively, kinematic measurements of neutral atomic hydrogen (HI), which naturally resides at the large disk radii that dominate the angular momentum. The SKA has a unique opportunity to become the world-leading facility for angular momentum studies due to its ability to measure the resolved and/or global HI kinematics in very large and well-characterised galaxy samples. These measurements will allow, for example, (1) a very robust determination of the two-dimensional distribution of galaxies in the (M,j)-plane, (2) the largest, systematic measurement of the relationship between M, j, and tertiary galaxy properties, and (3) the most accurate measurement of the large-scale distribution and environmental dependence of angular momentum vectors, both in terms of norm and orientation. All these measurements will represent exquisite tools to build a next generation of galaxy evolution models.