Circular words, also known as necklaces, are combinatorial objects closely related to linear words. A brief history of circular words is given, from their early conception to present results. We introduce the concept of a level word, that being a word containing a equal or roughly equal amount of each letter. We characterize exactly the lengths for which level square free circular words on three letters exist. This is accomplished through a modification of Shur’s construction of square-free circular words. A word on two letters is called a Frankel-Simpson word if the only squares it contains are 00, 11, and 0101. Using the result mentioned above and several computer searches, we characterize exactly the lengths for which circular Frankel-Simpson words exist, and give an example or construction for each. / Graduate