The main purpose of this book is to present the basic theory and some recent de- velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + AiU(i)(t) = 0, t 0, { U(k)(O) = Uk, 0 k n-l. where AQ, Ab . . ., A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc., can be trans- lated into this form by regarding the partial...