This book reproduces J-P. Serre's 1964 Harvard lectures. The aim is to introduce the reader to the "Lie dictionary": Lie algebras and Lie groups. Special features of the presentation are its emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on p-adic fields. Some knowledge of algebra and calculus is required of the reader, but the text is easily accessible to graduate students, and to mathematicians at large. TOC:Part I: Lie Algebras: Lie Algebras: Definition and Examples; Filtered Groups and Lie Algebras; Filtered Groups and Lie Algebras; Universal Algebra of a Lie Algebra; Free Lie Algebras; Nilpotent and Solvable Lie Algebras; Semisimple Lie Algebras; Representations of sln.- Part II: Complete Fields: Analytic Functions; Analytic Manifolds; Analytic Groups; Lie Theory.

Lie Algebras.- Lie Algebras: Definition and Examples.- Filtered Groups and Lie Algebras.- Universal Algebra of a Lie Algebra.- Free Lie Algebras.- Nilpotent and Solvable Lie Algebras.- Semisimple Lie Algebras.- Representations of .- Lie Groups.- Complete Fields.- Analytic Functions.- Analytic Manifolds.- Analytic Groups.- Lie Theory.