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LINEAR equations play an important part, not only in mathe matics itself, but also in many fields in which mathematics is used. The actual pro cess of setting up the equations and of interpreting the solution is one which more properly belongs to that field, and in any case is a problem of a different nature altogether.
The theory of Lie groups rests on three pillars: analysis, topology and algebra. Correspondingly it is possible to distinguish several phases, overlapping in some degree, in its development. It also allows one to regard the subject from different points of view, and it is the algebraic standpoint which has been chosen in this tract as the most suitable one for a first introduction to the subject.
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