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The goal of the first chapter is to express the main achievements in use of the Jahn-Teller effect (JTE) and pseudo JTE (PJTE) in search of materials with enhanced or novel properties, are presented as a part of what is known as materials science. The hallmark of this entire chapter is the commitment to identify situations in which waves are produced and provide a systematic classification of such convective instabilities together with a description of related features based on advanced numerical simulations. The quality and mechanical or electrical properties of the resulting solids and...