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<p>This monograph is an introduction into a new and fast developing field on the crossroads of infinite-dimensional Lie algebra theory and contemporary mathematical physics. It contains a self-consistent presentation of the theory of Krichever-Novikov algebras, Lax operator algebras, their interaction, representation theory, relations to moduli spaces of Riemann surfaces and holomorphic vector bundles on them, to Lax integrable systems, and conformal field theory.</p>
<p>For beginners, the book provides a short way to join in the investigations in these fields. For experts, it sums up the recent advances in the theory of almost graded infinite-dimensional Lie algebras and their applications.<br>The book may serve as a base for semester lecture courses on finite-dimensional integrable systems, conformal field theory, almost graded Lie algebras. Majority of results are presented for the first time in the form of monograph.</p>