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Learn algebraic number theory in this graduate-level lecture from IMPA's 2025 Summer School, where Professor Hossein Movasati covers fundamental concepts including rings, fields, characteristics, and the ring of integral algebraic numbers. Explore algebraic integers, the ring of algebraic integers of a number field, bases and discriminants, ideals, prime ideals, class groups, unique factorization, ideal norms, ramification, quadratic fields, quadratic reciprocity law, cyclotomic fields, Dirichlet's unit theorem, and zeta functions and L-series of number fields. Drawing from renowned references like Borevich and Shafarevich's Number Theory and Endler's Teoria dos Números Algébricos, master key theoretical foundations through this comprehensive first lecture in the series.
