The study of braids started in the early 20th century with the motivation of revealing properties of knots and links. The Artin braid group gives an algebraic tool to analyze the braid actions and the equivalence of braids. Later, a variation of ordinary braids, the annular braids, was introduced with additional rules added. In this thesis, we give three presentations to describe the annular braid group. We also use the annular braid group as a medium to abstract the braids in maypole dances and therefore apply an algebraic analysis. Finally, we discuss some essential properties embedded in the maypole braids, which are related to the invariants of annular braids - the crossing number and the step number.