This book contains the notes of three lecture series presented din the first semester of a year-long programme in algebraic model theory, organised by the Fields Institute for research in mathematical sciences during the academic year 1996-97. The lectures on differential fields (A. Pillay), o-minimality (P. Speisegger) and tame congruence theory (M. Clasen and M. Valeriote) present recent developments in these areas: in particular, the second lecture discusses the problem of adding the exponential function to certain o-minimal expansion of real numbers, and the third lecture also contains applications to the study of residually small varieties. A minimal knowledge of these topics is assumed.

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