The finite subgroups of SL (3 , F¯)

We attempt to give a complete exposition of the classification of the finite subgroups of SL (3 , F¯) , where F¯ is a separably closed field of characteristic not dividing the order of the finite group, in contemporary language, completing some of the proofs of Blichfeldt from the early twentieth century. The classification—originating from Jordan, Klein, Valentiner—has applications in algebraic geometry, number theory and mathematical physics.