الفهرس 
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Abstract
In this thesis we discuss the relation between Steiner triple systems ?STSs? and the algebraic structure called Steiner loops or briefly sloops. Also, we collect the interesting properties of Steiner loops, which are discussed by Quackenbush. Also, we have studied the relation between the triple systems associated with the direct product of sloops and the two types of products of triple systems. The second chapter is concerned with the concepts of solvability and nilpotence for sloops and SQSskeins, we have shown that the class of all solvable sloops of orders <U+F0A3> n forms a variety. Also, we have proven that the variety of nilpotent sloops of class n contains the variety of solvable sloops of order <U+F0A3> n. We classified the class of all sloops of cardinality 16 according to the shape of its congruence lattice into 5 classes, and we construct an extension from each nonsimple SL(16) to an SQSskein with the same congruence lattice of SL(16). Also, we will improve this result by showing that each nonsimple sloop of cardinality 16 can be extended to a nonsimple SQSskein for each possible congruence lattice. Finally, an example was given for all possible cases. Starting with any nonsimple sloop of cardinality 16, any non simple possible SQSskein can be constructed.