  These 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.
