I apologise in advance if the title is not clear, but I don't know the exact name of the subject I'm looking for.
I started reading Dirac's "Lectures on Quantum Mechanics", and it sparked my interest on the formalism of the generalised Hamiltonian, when the equations for the momenta lead to constraint equations of the form $\phi(p,q) = 0$. It did a very good job of explaining this "constraint" formalism and the Dirac bracket.
However, I am having trouble when it goes on to the generalisation in field theory. Indeed, all the derivatives are changed by functional derivatives, and I am not very comfortable with those yet. So I would like to ask if there exists other books, which may go into more detail about this "generalised hamiltonian formalism", especially in the field theory part. I wasn't able to find any resources mainly due to the fact that I don't know the name of this formalism.