Buchdahl is distinguished for his work on optical Aberration Coefficients and on the equations of General Relativity. His book on Aberration Coefficients is a monument of algebraic skill and perseverance; its publication by the Clarendon Press was subsidized by the Warren Fund of the Royal Society. His papers on relativity have led to some new results, especially on the behaviour of spherical masses under conditions of extremely high pressure. He is also author of a book on thermodynamics, and distinguished by the quality of his teaching of theoretical physics.