Topics range from introductory lectures on algebraic cycles to more advanced material in this collection of lecture notes from the Proceedings of the Grenoble Summer School, 2001. The advanced lectures are grouped under three headings: Lawson (co)homology, motives and motivic cohomology and Hodge theoretic invariants of cycles. As the lectures were intended for non-specialists, many examples have been included.

The NATO Advanced Study Institute on "The Arithmetic and Geometry of Algebraic Cycles" was held at the Banff Centre for Conferences in Banff (Al- berta, Canada) from June 7 until June 19, 1998. This meeting was organized jointly with Centre de Recherches Mathematiques (CRM), Montreal, as one of the CRM Summer schools which take place annually at the Banff Center. The conference also served as the kick-off activity of the CRM 1998-99 theme year on Number Theory and Arithmetic Geometry. There were 109 participants who came from 17 countries: Belgium, Canada, China, France, Germany, Greece,...

The NATO Advanced Study Institute on "The Arithmetic and Geometry of Algebraic Cycles" was held at the Banff Centre for Conferences in Banff (Al- berta, Canada) from June 7 until June 19, 1998. This meeting was organized jointly with Centre de Recherches Mathematiques (CRM), Montreal, as one of the CRM Summer schools which take place annually at the Banff Center. The conference also served as the kick-off activity of the CRM 1998-99 theme year on Number Theory and Arithmetic Geometry. There were 109 participants who came from 17 countries: Belgium, Canada, China, France, Germany, Greece,...

Das Buch wendet sich an alle, die in die klassischen Themen der Zahlentheorie einsteigen wollen. Viel Wert wird auf die konkrete Berechenbarkeit bei allen Problemlosungen gelegt. So gibt es auch Abschnitte uber moderne Primzahltests und Faktorisierungsalgorithmen und am Ende des Buches wird ein Weg zur Bestimmung der Klassenzahl der quadratischen Zahlkorper aufgezeigt.
Im Rahmen der Bachelor-/Master-Studiengange eignet sich das Buch als Grundlage fur zwei Semester: ein Aufbaumodul in elementarer Zahlentheorie mit einem Vertiefungsmodul in algebraischer Zahlentheorie.

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