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This monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic.  While the theorems and proofs included can be found throughout the existing literature, this is the first book to collect them in a single volume.  Details omitted from the original sources, along with additional computations and explanations, have been added to foster a stronger understanding of the theory of nilpotent groups and the techniques commonly used to study them.  Topics discussed include collection processes, normal forms and embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie algebras, decision problems, and nilpotent groups of automorphisms.  Requiring only a strong undergraduate or beginning graduate background in algebra, graduate students and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable resource.

Mathematics. --- Associative rings. --- Rings (Algebra). --- Group theory. --- Topological groups. --- Lie groups. --- Group Theory and Generalizations. --- Associative Rings and Algebras. --- Topological Groups, Lie Groups. --- Rings (Algebra) --- Algebraic rings --- Ring theory --- Algebraic fields --- Algebra. --- Topological Groups. --- Groups, Topological --- Continuous groups --- Mathematics --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups