This book gives a short and basic treatment of Diophantine Equations. These are defined here as polynomials with one or more variables in finite powers and integer or rational coefficients.In chronological order with former books on Pythagorean Tripies and Euclidean Sequences this third text is written for all who are interested in basic mathematics and have an elementary knowledge of algebra. Especially it may be of interest for the student who begins to study the elements of number theory and history of mathematics. The book is dedicated to Diophantos because his famous Arithmetica is perhaps the first comprehensive and outstanding treatment of algebra. For apart Diophantos has published results of older philosophers and mathematicians. But there is certainly an important own contribution. Fortunately some of his Books were copied many centuries and so preserved until now.