Projectively dual varieties

During several centuries various reincarnations of projective duality have inspired research in algebraic and differential geometry, classical mechanics, invariant theory, combinatorics, etc. On the other hand, projective duality is simply the systematic way of recovering the projective variety from the setof its tangent hyperplanes. In this survey we have tried to collect togetherdifferent aspects of projective duality and points of view on it. We hope, thatthe exposition is quite informal and requires only a standard knowledge ofalgebraic geometry and algebraic (or Lie) groups theory. Some chapters are,however, more difficult and use the modern intersection theory and homologyalgebra. But even in these cases we have tried to give simple examples andavoid technical difficulties.