This lecture is aimed at an audience who is familiar with some basic quantum mechanics. Its aim is to convey the basic ideas and show some applications of Bohmian mechanics in a rather accessible way. Consequently it sometimes ignores subtleties and demonstrates things in a simplified way. For a more thorough account we refer to the literature that can be found in the script to the lecture. Script available online at:http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/files/script_An_Introduction_to_BM.pdf