Al-khorezmi his background, his personality his work and his influence -- Algorithms in modern mathematics and computer science -- What are the gains of the theory of algorithms -- On inductive synthesis of programs -- Expanding constructive universes -- The logical approach to programming -- The structural synthesis of programs -- On finding invariant relations of program -- What can we do with problems of exhaustive search? -- The algorithmic complexity of linear algebras -- Algorithms in various contexts -- Role of a notion of algorithm in the arithmetic language semantics -- From logicism to proceduralism (an autobiographical account) -- Abstract computability on algebraic structures -- Algorithms and algebra -- On formal transformations of algorithms -- What should we do having proved a decision problem to be unsolvable? -- On the experience of riding two horses in programming -- Church-rosser transformers and decidable propertis of tree processing -- Supplement 1 summaries of oral presentations -- Supplement 2 technical program -- Supplement 3 publications on the symposium -- List of participants -- Supplement 5 photoillustrations.