I am a graduate student of Mathematics and we have a course in this semester on linear algebra which includes bilinear forms and quadratic forms.The following are the things we need to study:
$1.$ Change of basis in bilinear form.
$2.$Quadratic forms and polarisation.
$3.$ Normal form.
$4.$Positive definite forms.
$5.$ Sylvester's law of inertia.
$6.$ Matrix of positive definite form.
Our course instructor is following the book by Vinberg but it is difficult for me.Can someone suggest any text or lecture note on quadratic form that discusses these topics?Also I would be grateful if someone suggests some problems on these topics.