A short summary of binary quadratic forms is provided. This includes classes of forms under various equivalence relations, the relationship between the existence of a primitive representation of an integer n by a binary quadratic form Q and an ideal factorization of  construction of the automorph matrix, Ardnt’s composition algorithm, Gauss’ bilinear transformation, Bhargava cubes, and proof of the isomorphism between the ideal class group and the class group of forms.