In our work, the aim was to develop the new efficient sorting algorithms to reduce the cost and complexity of existing algorithms. In the work, new sorting methods have been proposed, their algorithms have been derived and performance has been compared with well known existing methods. It was discovered that the algorithms proposed in this book is relatively simpler and efficient. In preparing this book, we have made every effort to simplify the presentation wherever possible, striving for shorter and focused approach. We are hopeful that students in the same discipline and posterity shall find our book of substance and value in future. We have tried our best to propose the algorithms which are efficient and simple as well.