While the theory of finite fields emerged as an independent discipline at the end of the 19-th century, aspects of the subject can be traced back at least to the middle of the 17-th century. It is our intention to present here a survey of highlights of finite field theory as they emerged in the 18-th and 19-th centuries, culminating in a description of Eliakim Hastings Moore’s [2139], which began the study of abstract finite fields.