On gaussian forms and ternary quadratic form matrices

This is an exposition of the first two sections of Chapter 6, The Polygonal Number Theorem of the book The Queen of Mathematics by W. S. Anglin. This book was published in 1995 by Kluwer Academic Publishers. The paper deals with positive definite quadratic forms in two and three variables also known as the gaussian forms and ternary quadratic forms respectively. It discusses on concepts and theorems regarding equivalence between gaussian forms and ternary quadratic forms, reduction of gaussian forms, important properties and results satisfied by gaussian forms, ternaries and their equivalent. The discussion focuses on some of the preliminary concepts and theorems needed in understanding the Cauchy\u27s proof of Fermat\u27s polygonal number conjecture