Electroweak Processes in External Electromagnetic Fields This book explores the intersection of particle physics astrophysics and cosmology known as astroparticle physics. Extreme electromagnetic conditions present in puslars and other stars allow for investigations of the role of quantum processes in the dynamics of astrophysical objects and in the early Universe. Based in part on the authors own work this book systematically describes several methods of calculation of the effects of strong electromagnetic fields in quantum processes using analytical solutions of the Dirac equation and Feynmann diagrams at both the loop and tree levels. The consideration is emphasized at the two limiting cases: the case of a very strong magnetic field and the case of a crossed field. The presentation will appeal to graduate students of theoretical physics with prior understanding of Quantum Field Theory (QFT) and the Standard Model of Electroweak Interactions as well as specialists in QFT wishing to know more about the problems of quantum phenomena in external electomagnetic fields. Solutions of the Dirac Equation in an External Electromagnetic Field Fermion Propagator in an External Electromagnetic Field Generalized Two Point Loop Amplitude in an External Electromagnetic Field Tree Level Quantum Processes in an External Field Loop Level Quantum Processes in an External Electromagnetic Field.