This volume presents selected contributions from the seminar “Mathematical Models and Integration Methods,” highlighting recent advances in differential equations, mathematical modeling, and modern analytical techniques. The topics cover a wide range of problems, including vortex structures in ferromagnets, wave propagation in inhomogeneous media, reciprocal transformations of heat equations, nonlinear resonance phenomena, and composite beam analysis. The collection also includes studies on the exponential map of vector fields, sedeonic models in superconductivity, and transformations in relativistic systems. Most contributions are from leading Russian researchers, complemented by papers from international participants. The book is intended for specialists in applied mathematics, mathematical physics, and engineering disciplines interested in contemporary modeling approaches and integration methods.