This volume contains contributions arising from lectures and related discussions held at the meeting on ‘Differential Equations: Inverse and Direct Problems’, which took place at Cortona, 21st-25th June 2004. Almost all of fourteen contributions contain original results; they do not just survey and explain results already published elsewhere. They cover a wide scope of up-to-date topics from the field of differential equations. Thus there are papers dealing with abstract differential equations in Banach spaces, linear and nonlinear semigroup theory, direct and inverse problems for non-degenerate and degenerate equations, differential equations with Wentzell boundary conditions and a deep study of equations of mathematical physics (e.g. from superconductivity and phase transition problems). The book will be an interesting and stimulating read for research workers in the field.