This book - based on the Conference on Differential Equations, held in Bologna - provides information on current research in parabolic and hyperbolic differential equations. Presenting methods and results in semigroup theory and their applications to evolution equations, this book focuses on topics including: abstract parabolic and hyperbolic linear differential equations; nonlinear abstract parabolic equations; holomorphic semigroups; and Volterra operator integral equations. With contributions from international experts, "Differential Equations in Banach Spaces" is intended for research mathematicians in functional analysis, partial differential equations, operator theory and control theory; and students in these disciplines.