Maple packages and Java applets for classification problems in geometry and algebra. I briefly describe an on-going project at Utah State University to create Maple software and Java applets for use in classification problems in geometry and algebra. The first problem we are currently working on deals with Petrov’s remarkable classification of all 4-dimensional local group actions which admit a Lorentz invariant metric; the second focuses on the classification of low dimensional Lie algebras. The software which supports our work on these two classification problems is part of the Maple suite of software packages called Vessiot, an integrated collection of Maple programs for computations in differential geometry, Lie algebras and the variational calculus on jet spaces.