This book discusses the ways in which the algebras in a locally finite quasivariety determine its lattice of subquasivarieties.nbsp; The book starts with a clear and comprehensive presentation of the basic structure theory of quasivariety lattices, and then develops new methods and algorithms for their analysis. nbsp;Particular attention is paid to the role of quasicritical algebras.nbsp; The methods are illustrated by applying them to quasivarieties of abelian groups, modular lattices, unary algebras and pure relational structures.nbsp; An appendix gives an overview of the theory of quasivarieties.nbsp; Extensive references to the literature are provided throughout.