The book is devoted to applications of nonstandard methods of analysis to the theory of vector lattices. Much attention is paid to the problem of combining infinitesimal and Boolean-valued concepts to studying classical problems of the theory of vector lattices related to constructing concrete representations of abstract functional-analytic objects: Banach–Kantorovich spaces, dominated operators, vector measures, integral operators, etc.

This book is intended for those interested in modern applications of nonstandard analysis to problems of functional analysis.