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The book's main content is from Dr. Jun Lin'sdissertation submitted to the University of NewHampshire in partial fulfillment of the requirementsfor the PhD degree in physics in September 2001.Some theoretical models of solar eruptions derivedfrom previous works that involve a loss ofequilibrium of the coronal magnetic field arepresented. These models consist of a magnetic fluxrope nested within an arcade of magnetic loop.Before the eruption, the flux rope floats in thecorona under a balance between magnetic compressionand tension forces. When an eruption occurs, themagnetic compression exceeds the magnetic tensionand causes the flux rope to be thrown outwards, awayfrom the Sun. Three important factors which impactthe occurrence and evolution of the eruptiveprocesses are investigated. These factors aremagnetic reconnection, new emerging flux, and thelarge scale curvature of the flux rope. The resultssuggest that the catastrophic loss of equilibriumin the coronal magnetic configuration plays animportant role in triggering the eruption, andreconnection in the current sheet created by thecatastrophe helps the process to eveolve smoothly.