Analytic and algebraic geometry 1

Annual Conferences in Analytic and Algebraic Geometry have been organized by Facul-ty of Mathematics and Computer Science of the University of Łódź since 1980. Until now, proceedings of these conferences (mainly in Polish) have comprised educational materials describing current state of a branch of mathematics, new approaches to known topics, and new proofs of known results (http://konfrogi.math.uni.lodz.pl/). The volume include new results and survey articles concerning real and complex alge-braic geometry, singularities of curves and hypersurfaces, invariants of singularities (the Milnor number, degree of C0-sufficiency), algebraic theory of derivations and oth-ers topics. English translation of the Polish version of an article by Stanisław Łojasiewicz (1926-2002) devoted to the famous Hironaka theorem on resolution of singularities. It con-tains his original approach to the problem in the case of curves and coherent analytic sheaves on 2-dimensional manifolds. This interesting article has not yet been available in English. The volume is dedicated to the memory of Stanisław Łojasiewicz. We are deeply in-debted to him for introducing the topics of analytic and algebraic geometry in the Łódź mathematical centre.