Robb studied at Queen's College in Belfast and at St John’s College in Cambridge. He then proceeded to University of Göttingen, where guided by Woldemar Voigt, he wrote his dissertation on the Zeeman effect. He also worked under J. J. Thomson at the Cavendish Laboratory. The Croix de Guerre was awarded to him, and in 1921 he became a fellow of the Royal Society. 
He is known for his four works on special relativity (1911, 1914, 1921, 1936) where he derived a spacetime formalism of the theory in an axiomatic-geometric way. Robb therefore was sometimes called the "Euclid of relativity". In the first of these works he used a hyperbolic angle to introduce the concept of rapidity which clarified the relativistic velocity-addition formula. He also showed that the kinematic space of velocities is hyperbolic, that is, that "instead of a Euclidean triangle of velocities, we get a Lobachevski triangle of rapidities". However, contrary to the scientific mainstream, he believed that the works of Joseph Larmor and Hendrik Lorentz were more important for relativity than the works of Albert Einstein and Hermann Minkowski.
- Robb, Alfred (1911). Optical geometry of motion, a new view of the theory of relativity. Cambridge: Heffner & Sons.
- Robb, Alfred (1914). A theory of time and space. Cambridge: University Press.
- Robb, Alfred (1921). The absolute relations of time and space. Cambridge: University Press.
- Robb, Alfred (1936). Geometry Of Time And Space. Cambridge: University Press.
- Larmor, J. (1938). "Alfred Arthur Robb. 1873-1936". Obituary Notices of Fellows of the Royal Society 2 (6): 315–326. doi:10.1098/rsbm.1938.0013.
- "Robb, Alfred Arthur (RB894AA)". A Cambridge Alumni Database. University of Cambridge.
- Sanchez-Ron, José M. (1987). "The reception of special relativity in Great Britain". In T. F. Glick. The Comparative Reception of Relativity. Berlin: Springer. pp. 27–58. ISBN 90-277-2498-9.
- A. J. Briginshaw, The axiomatic geometry of Space-Time: An assessment of the work of A. A. Robb, Centaurus 22, pp. 315-323 (1979)
- Walter, Scott (1999). "The non-Euclidean style of Minkowskian relativity". In J. Gray. The Symbolic Universe: Geometry and Physics. Oxford: University Press. pp. 91–127. ISBN 0-19-850088-2.
- Robb (1911) Optical Geometry of Motion, p.27.
- Sanchez-Ron, pp. 46-49