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In this short review, we discuss the approach of the commutator algebra ofcovariant derivative to analyse the gravitational theories, starting from thestandard Einstein's general theory of relativity and focusing on the Rastalltheory. After that, we discuss the important role of the torsion in thismathematical framework. In the Appendix of the paper we analyse the importanceof the nascent gravitational wave astronomy as a tool to discriminate among thegeneral theory of relativity and alternative theories of gravity.

The commutator algebra of covariant derivative as general framework for extended gravity. The Rastall theory case and the role of the torsion