2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74310We highlight recent progresses in the study of the Weil-Petersson (WP) geometry of finite dimensional Teichmüller spaces. For recent progress on and the understanding of infinite dimensional Teichmüller spaces the reader is directed to the recent work of Teo-Takhtajan. As part of the highlight, we also present possible directions for future investigations.18 pagesDifferential Geometry32G15; 30F10text