This thesis is an extensive examination of a graduate level monograph, Counter-Free Automata by McNaughton and Papert, to develop a deep understanding of the subject. This book is about many subclasses of type 3 languages and it proves all of these subclasses are equivalent. We have explored chapters 1 to 8 and 10. The real goal of this thesis is to solve as many problems at the end of each chapter in the book as possible. The thesis rehashes the discussion in the text of the nine chapters mentioned above. It is to be noted the text has no solution in the back of the book nor do any solutions appears to be available online. Since half or more of the problems have been solved in this undertaking, in effect a substantial beginning of a solution manual has been produced.