Gandhi, Raj2021-08-232021-08-232021-08-23http://hdl.handle.net/10393/42566http://dx.doi.org/10.20381/ruor-26786In this thesis, we compute minimal presentations in terms of generators and relations for the oriented cohomology rings of several semisimple linear algebraic groups of ranks 1 and 2 over algebraically closed fields of characteristic 0. The main tools we use in this thesis are the combinatorics of Coxeter groups and formal group laws, and recent results of Calm\`es, Gille, Petrov, Zainoulline, and Zhong, which relate the oriented cohomology rings of flag varieties and semisimple linear algebraic groups to the dual of the formal affine Demazure algebra.enAlgebraic groupsAlgebraic geometryAlgebraic oriented cohomology theoriesDemazure operatorFormal group lawThesis