The most important results for the development of science are: 1. the complete solution of the problem of the stability of isometries, 2. the new method for sloving Kaplansky's problem of describing linear invertibility preservers (the reduction to the problem of characterizing idempotent preservers), 3. the solution of the problem of the stability of homomorphisms on function algebras, 4. the characterization of the spectral distance preservers, 5. general techniques for linear preserver problems, 6. the characterization of isometries with respect to the numerical radius, 7. the improvement of results on geometry of matrices, 8. the improvement of some linear preserver results (commutativity,numerical range), 9. the characterization of some non-linear preservers (commutativity,triangularizability), 10. the solution of the problem of reflexivity of elementary operators of length one.