On Monday, a team of mathematicians announced that the most complex exceptional Lie group E8 had been mapped. Their mapping of E8 involved 77 hours of calculation on a supercomputer and 60 gigabytes of results. The New York Times article on this described E8 as "the most complicated of the 'exceptional simple Lie groups'." Of course, this is a strictly technical meaning of the term "simple".
(The "Lie" in Lie groups rhymes with "bee" and not with "by", since it comes from the name of the Norwegian mathematician Sophus Lie)
From the point of view of classification, Lie groups are interesting, because they draw from several areas of mathematics. They are groups, which puts them in algebra; they involve continuity, a concept drawn from analysis; and they involve symmetry, a concept drawn from geometry. In addition, Lie groups are used in several areas of mathematical physics, including string theory.
Lie groups are classed in 512.482 Lie algebras and groups.