Three lessons on the Painleve property and the Painleve equations

While this school focuses on discrete integrable systems we feel it necessary, if only for reasons of comparison, to go back to fundamentals and introduce the basic notion of the Painleve property for continuous systems together with a critical analysis of what is called the Painleve test. The extension of the latter to what is called the poly-Painleve test is also introduced. Finally we devote a lesson to the proof that the Painleve equations do have the Painleve property.