A $~$\\lambda$~$ expression is something of the form $~$\\lambda x.f(x)$~$, which means "take in an input $~$x$~$, and return $~$f(x)$~$\. For example, $~$\\lambda x.x+1$~$ takes in a number and returns one more than it\. A $~$\\lambda$~$ expression can have multiple inputs; e\.g\. $~$\\lambda x.\\lambda y.x+y$~$ takes in two numbers and returns their sum\. We can also write this as $~$\\lambda xy.x+y$~$; "$~$\\lambda xy$~$" is simply a shorthand for "$~$\\lambda x.\\lambda y$~$\."

I think it's confusing to introduce multi-argument functions before talking about currying. This makes it seem as though multi-argument functions are an intrinsic part of the lambda calculus, rather than just functions that return other functions.