In this dissertation, we consider decoupling inequalities. The study of this topic originated from classical problems in number thoery, for example, Waring's problem, Wely sum estimate, and estimates of the Riemann zeta function. We prove sharp $l^qL^p$ decoupling inequalities for $p, q \in [2,\infty)$ and arbitrary tuples of quadratic forms. estimates. The proof of our main result is based on scale-dependent Brascamp–Lieb inequalities.