In this book for the first time the authors study the new type of Euclid squares in various planes like real plane, complex plane, dual number plane, special dual like number plane and special quasi dual number plane.

There are six such planes and they behave distinctly. From the study it is revealed that each type of squares behave in a different way depending on the plane.

We define several types of algebraic structures on them. Such study is new, innovative and interesting. However for some types of squares; one is not in a position to define product. Further under addition these squares from a group.

One of the benefits is addition of point squares to any square of type I and II is an easy translation of the square without affecting the area or length of the squares. There are over 150 graphs which makes the book more understandable.