ABSTRACT
This chapter explains group theory in particle, nuclear, and Hadron physics by using simple examples from physics and mathematics. A group is a set of elements obeying a single law of composition which must satisfy certain constraints. The group is comprised of two entities: a set and a binary operation. When the existence of a group G is asserted, the presence of an associated binary operation is implicitly implied. The chapter provides a table that express the entire group structure of a finite-dimensional group in a composition table. The composition tables are a useful graphical manner of displaying the structure of the group wherein the number of group elements (the order of the group) is small. The group may be considered to be a subgroup of itself, but it is denominated a trivial subgroup or improper subgroup. The identity is also a subgroup but again is called trivial.
