We are surrounded by uncountable geometric shapes and each one of them has its algebraic representation. The difficulties of finding the matching between them are known but, today we are privileged by the use of computer programs. This book provides a brief introduction to quasi-quadrilaterals(a new type of closed or open curves) and their algebraic representations and their properties. It will challenge many mathematicians and specialists of other sciences to think and work for new techniques and methods or algorithms to answer the questions and problems raised from the beginning to the end. It is a new window in the Euclidean Geometry which will lead many mathematicians, engineers and researchers to make new discoveries. The applications of the book are of a wide range: firstly, in mathematics (develop new techniques and methods or algorithms); secondly in engineering and physics sciences, where the use of quasi-rectangles/trapezoids and of the respective geometric construction techniques, extreme accuracy and the proper use of drafting instruments are very important. It is a great help to engineering designers to effectively solve their problems of improving product quality .