  In this book, for the first time we introduce the notion of neutrosophic
algebraic structures for groups, loops, semigroups and groupoids; and also
their neutrosophic N-algebraic structures.
  One is fully aware of the fact that many classical theorems like Lagrange,
Sylow and Cauchy have been studied only in the context of finite groups. Here
we try to shift the paradigm by studying and introducing these theorems to
neutrosophic semigroups, neutrosophic groupoids, and neutrosophic loops.
  This book has seven chapters. Chapter one provides several basic notions to
make this book self-contained. Chapter two introduces neutrosophic groups and
neutrosophic N-groups and gives several examples. The third chapter deals with
neutrosophic semigroups and neutrosophic N-semigroups, giving several
interesting results. Chapter four introduces neutrosophic loops and
neutrosophic N-loops. We introduce several new, related definitions. In fact we
construct a new class of neutrosophic loops using modulo integer Z_n, n > 3,
where n is odd. Several properties of these structures are proved using number
theoretic techniques. Chapter five just introduces the concept of neutrosophic
groupoids and neutrosophic N-groupoids. Sixth chapter innovatively gives mixed
neutrosophic structures and their duals. The final chapter gives problems for
the interested reader to solve.
