This is the last of three volumes about "Simple Lie Algebras over Fields of Positive Characteristic"by Helmut Strade, presenting the state of the art of the structure and classification of Lie algebras over fields of positive characteristic. In this monograph the proof of the Classification Theorem presented in the first volumeis concluded.Itcollects all the important results on the topic whichcan be found only in scatteredscientific literaturso far.