Introduction to Morrey spaces

The present informal set of notes covers the material that has been presented by the author in a series of lectures for the Doctoral School in Mathematics of the Southern Federal State University of Rostov-on-Don in the Fall of 2020 and that develops from the first part of the notes that collect the material of the lectures of the author at the Eurasian National University, Astana, Kazakhstan in the Spring of 2012. The aim is to present some elementary classical properties of Morrey spaces and some corresponding approximation results by smooth functions.