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In this thesis we study dynamic of magnetic monopoles from Lagrangian densityin Yang-Mills-Higgs field theory. In particular, we discuss BPS (BogomolnyPrasad Sommerfield) magnetic monopoles, described by SU(N) Bogomolny equations,which has field equations in form of non-linear coupled matrix field equations.One of the methods to simplify SU(N) Bogomolny equations is by using harmonicmaps $CP^{(N-1)}$. This method has relation with $Gr(n,N)} \sigma$-model andcan transform SU(N) Bogomolny equation into more simple scalar field equationsthat depends only on one variable. As an example, we consider the case of SU(2)Bogomolny equation.

Application of Harmonic Maps $CP^{(N-1)}$ on SU(N) Bogomolny Equation for BPS Magnetic Monopoles