Induced representations of locally compact groups Locally compact groups arise in many diverse areas of mathematics the physical sciences and engineering and the presence of the group is usually felt through unitary representations of the group. This observation underlies the importance of understanding such representations and how they may be constructed combined or decomposed. Of particular importance are the irreducible unitary representations. In the middle of the last century G.W. Mackey initiated a program to develop a systematic method for identifying all the irreducible unitary representations of a given locally compact group G. We denote the set of all unitary equivalence classes of irreducible unitary representations of G by G. Mackeys methods are only effective when G has certain restrictive structural characteristics; nevertheless time has shown that many of the groups that arise in important problems are appropriate for Mackeys approach. The program Mackey initiated received contributions from many researchers with some of the most substantial advances made by R.J. Blattner and J.M.G. Fell. Fellswork is particularly important in studying Gas a topological space. At the core of this program is the inducing construction which is a method of building a unitary representation of a group from a representation of a subgroup