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A text for a year-long introduction to arithmetic geometry, leading the reader in a logical progression from the local to the global properties of rings and curves through the study of class groups and of the Riemann-Roch theorem. Emphasizes the connection between algebraic number and algebraic curve theory, with worked examples and exercises. Includes reference appendices and a glossary. For graduate students and research mathematicians.

Algebraic geometry --- 512.75 --- Arithmetic problems of algebraic varieties. Rationality questions. Zeta-functions --- 512.75 Arithmetic problems of algebraic varieties. Rationality questions. Zeta-functions --- Arithmetical algebraic geometry --- Algebraic geometry, Arithmetical --- Arithmetic algebraic geometry --- Diophantine geometry --- Geometry, Arithmetical algebraic --- Geometry, Diophantine --- Number theory --- Arithmetical algebraic geometry. --- 31.51 algebraic geometry. --- Algebraische Geometrie --- Arithmetische Geometrie --- Getaltheorie. --- Algebraïsche meetkunde. --- Géométrie algébrique arithmétique. --- Géométrie algébrique arithmétique.