Chapter 7 of the book "Quantum Optics" by Gerry and Knight (published by Cambridge University Press) is decidated to quadrature squeezing. Section 7.2 contains a discuss of two-mode squeezing.
The frontmatter for this book is openly available. Quoting from this:
This text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first- and second-year graduate students.
The book review published in American Journal of Physics is also openly available.
Squeezing is realized in quantum optics through operators of the type $\hat a^\dagger \hat b^\dagger$, $\hat a\hat b$ and their commutator. The set closes on $su(1,1)$ but most of the mathematics - especially if you are interested in squeezing the boson vacuum $\vert 0\rangle$ - actually only requires patient use of raising and lowering operators. If you have experience with creation and destruction operators, you can bypass much of the more technical quantum optics stuff of the early chapters of Gerry and Knight and dive in directly to chapter 7, going back to the early chapters only if needed.