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Singularity theory is an area of mathematics at the crossroads of algebraic geometry, topology, and differential equations. § Initiated by Thom, Arnol'd and others in the 1970s, it quickly developed into a central area of mathematics. § Challenging problems on singularities were both a driving force and a beneficiary of the development of Gröbner basis methods in computer algebra. § This unique volume is a collection of recent original research by some of the leading figures of singularity theory of the last three decades. The articles highlight a large variety of techniques, ranging from theoretical methods to practical tools from computer algebra. § The articles reflect lectures given at a conference in honor of Gert-Martin Greuel on the occasion of his 70th birthday. Greuel himself made major contributions to the development of both singularity theory and computer algebra. § He was one of the founders of the computer algebra system SINGULAR, director of the Mathematical Research Institute Oberwolfach from 2002 to 2013, and he initiated the IMAGINARY exhibition bringing mathematics to the public. § Currently he is Editor-in-Chief of Zentralblatt MATH. § The book addresses researchers with connections to singularity theory and computer algebra from PhD. to expert level.§
