In this review we first outline the basics of transport theory and its recent generalization to offshell transport. We then present in some detail the main ingredients of any transport method using in particular the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) implementation of this theory as an example. We discuss the potentials used, the ground state initialization and the collision term, including the in-medium modifications of the latter. The central part of this review covers applications of GiBUU to a wide class of reactions, starting from pion-induced reactions over proton and antiproton reactions on nuclei to heavy-ion collisions (up to about 30 AGeV). A major part concerns also the description of photon-, electron-and neutrino-induced reactions (in the energy range from a few 100 MeV to a few 100 GeV). For this wide class of reactions GiBUU gives an excellent description with the same physics input and the same code being used. We argue that GiBUU is an indispensable tool for any investigation of nuclear reactions in which final-state interactions play a role. Studies of pion-nucleus interactions, nuclear fragmentation, heavy-ion reactions, hypernucleus formation, hadronization, color transparency, electronnucleus collisions and neutrino-nucleus interactions are all possible applications of GiBUU and are discussed in this article.

The article contains new results for spin-3/2 and -1/2 resonances. It specializes to the second resonance region, which includes the P11(1440), D13(1520) and S11(1535) resonances. New data on electroproduction enable us to determine the vector form factors accurately. Estimates for the axial couplings are obtained from decay rates of the resonances with the help of the partially conserved axial current (PCAC) hypothesis. We present cross sections to be compared with the running and future experiments. The article is self-contained and allows the reader to write simple programs for reproducing the cross sections and for obtaining additional differential cross sections.

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Background: Charged current pion production gives information on the axial formfactors of nucleon resonances.It also introduces a noticeable background to quasi-elastic measurements on nuclear targets.Purpose: Understand pion production in neutrino interactions with nucleons and the reaction mechanism in nuclei.Method: The Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) model is used for an investigation of neutrinonucleus reactions.

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