2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123554These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi-Yau manifolds in two different ways; as hypersurfaces in toric varieties and as local toric Calabi-Yau threefolds. These lecture notes supplement a mini-course that was given by the author at the Modave Summer School in Mathematical Physics 2005, and at CERN in 2007.63 pages, 15 figures; an older version of these notes was published in the Proceedings of the Modave Summer School in Mathematical Physics 2005High Energy Physics - Theorytext