Using the idea "Pastes" which is known to mathematicians as "Sets of transition functions", fiber bundle and differential geometric languages are re-defined. In terms of these, possible similarities between the gauge theories and the fiber bundle theories are systemetically discussed. In this work, all fiber bundle types over the Minkowski space-time with n time like infinite string singularities are rigorously determined. It is shown that if the structure group G is arcwise connected, the types of monopoles are determined by n direct sum of the first homotopy group $\pi_1(G)$ of G.