Part I. Lie theory and algebraic geometry -- Lie groups and semigroups -- Applications of Lie semigroups in analysis -- Embedding semigroups into Lie groups -- Algebraic varieties and semigroups -- Part II. The compact case -- Compact semilattices, partial orders and topology -- Compact semitopological semigroups -- Semigroupes affines semitopologiques compacts -- Compact semigroups with one-sided continuity -- Part III. Functional analysis on semigroups -- Measure algebras on semigroups -- Positive definite and related functions on semigroups -- Convolution semigroups and potential kernels on a commutative hypergroup -- Amenability of semigroups -- Part IV. Applications: Systems theory, number theory, probability, topology -- Applications of semigroups to geometric control theory -- The semigroup βℕ and its applications to number theory -- Probability measures on semigroups of nonnegative matrices -- Some trends and directions in the investigation of congruences on S(X) -- List of contributors.