Systems with competing energy scales are widespread and exhibit rich and subtle behaviour, although their systematic study is a relatively recent activity. This text presents lectures given at a NATO Advanced Study Institute reviewing the current knowledge and understanding of this fascinating subject, particularly with regard to phase transitions and dynamics, at an advanced tutorial level.
Both general and specific aspects are considered, with competitions having several origins; differences in intrinsic interactions, interplay between intrinsic and extrinsic effects, such as geometry...