<p>This textbook offers an elementary introduction to noncommutative rings and algebras. Beginning with the classical theory of finite-dimensional algebras, it then develops a more general structure theory of rings, grounded in modules and tensor products. The final chapters cover free algebras, polynomial identities, and rings of quotients.</p><p>Many results are presented in a simplified form rather than in full generality, with an emphasis on clear and understandable exposition. Prerequisites are kept to a minimum, and new concepts are introduced gradually and carefully motivated. <em>Introduction to Noncommutative Algebra</em> is thus accessible to a broad mathematical audience, though it is primarily intended for beginning graduate students and advanced undergraduates encountering the subject for the first time.</p><p>This new edition includes several additions and improvements, while preserving the original text’s character and approach.</p><p><strong>Praise for the first edition:</strong></p><p>“<em>It will soon find its place in classrooms</em>” — Plamen Koshlukov, Mathematical Reviews</p><p>“<em>Very well written</em> [...] <em>very pleasant to read</em>” — Veereshwar A. Hiremath, zbMATH</p><p>“<em>An excellent choice for a first graduate course</em>” — D. S. Larson, Choice</p>