The contents of the paper are to appear in book form shortly [ 4 ] and it has been given in the author＇s lectures at Abdug Salam School of Math Sci. GC Univ. Lahore, Pakistan in Feb. , 2011. We mean by the exhaustion principle that in a certain way, there is a rule which exhaust all the elements of a system, i. e. , a sort of classification. We shall illustrate this principle by significant examples. Since our examples are related to groups, the exhaustion is mostly of the form of a disjoint union of subsets Hd （ d ｜ n） exhausting the whole group G： G = ∪d/a Hd （disjoint）.
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