Introduction -- Deformations of singularities -- Standard bases -- Infinitesimal deformations -- Example: the fat point of multiplicity four -- Deformations of algebras -- Formal deformation theory -- Deformations of compact manifolds -- How to solve the deformation equation -- Convergence for isolated singularities -- Quotient singularities -- The projection method -- Formats -- Smoothing components of curves -- Kollár's conjectures -- Cones over curves -- The versal deformation of hyperelliptic cones -- References -- Index.