Suppose I have a set of random variables $X_1, X_2, \ldots, X_N$ which are described by known probability density functions (PDF's) $f_{X_1}, f_{X_2}, \ldots, f_{X_N}$. I want to derive a formula for the PDF $f_Y$ of a new variable $Y = g(X_1, X_2, \ldots, X_N)$, where $g$ is some known function.
Is there a book which describes how to do this? I've found, on the internet, how to compute e.g. the PDF of a sum of two random variables, or the PDF of a function of a single random variable. But I would like a more comprehensive, "cookbook" source.
Thanks.