The text consists of the lectures presented at the NATO ASI on "Algebras and Orders" held in 1991 at the Universite de Montreal. The lectures cover a broad spectrum of topics in universal algebra, Boolean algebras, lattices and orders, and their links with graphs, relations, topology and theoretical computer science. More specifically, the topics covered include: abstract clone theory; hyperidentities and hypervarieties; arithmetical algebras and varieties; Boolean algebras with operators; algebraic duality; model-theoretic aspects of partial algebras; free lattices; algebraic ordered sets; diagrams of orders; essentially minimal groupoids, and formalization of predicate calculus. Most of the papers are up-to-date surveys written by leading researchers, or topics that are either new or have witnessed recent substantial progress. The text is suitable for graduate students and researchers.