This lecture is intended as an introduction to selected state-of-the-art research topics in the field of molecular physics. A survey is given starting from fundamentals to the current state of research. It focusses on spectroscopic methods used to investigate molecular systems in the gas and condensed phase. Light-matter interaction will be reported to understand linear and nonlinear spectroscopic methods. Particularly the spectroscopy of cold molecules and the application of ultrashort laser pulses for investigating molecular dynamics will be discussed.