The theory of Lie algebras and algebraic groups has been an area of activeresearch in the last 50 years. It intervenes in many different areas ofmathematics : for example invariant theory, Poisson geometry, harmonicanalysis, mathematical physics. The aim of this book is to assemble in asingle volume the algebraic aspects of the theory so as to present thefoundation of the theory in characteristic zero. Detailed proofs are includedand some recent results are discussed in the last chapters. All theprerequisites on commutative algebra and algebraic geometry are included.