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