Propositional formulas 3 What are the difference between:

$A \implies (B \implies C)$, $\ (A \implies B) \implies C$, $\ A\land B \implies C$, $\ A \implies B \land C$, $\ (A \implies B)\land (B \implies C)$?

Why we can not write $A \implies B \implies C$?

And the same questions about:

$A \iff(B \iff C)$, $\ (A \iff B) \iff C$, $\ A\land B \iff C$, $\ A \iff B \land C$, $\ (A  \iff B)\land(B \iff C)$?

Why we can not write $A \iff B \iff C$?

Can someone explain me this ?
You can work out the differences with truth tables, or you can note that $p\to q$ is equivalent to $q\hbox{ OR NOT }p,$ and for the second case, that $p\leftrightarrow q$ is equivalent to $(p\hbox{ AND }q)\hbox{ OR }(\hbox{ NOT }p\hbox{ AND NOT }q$).

Then, once you have established that brackets can change the meaning of an expression, writing something like $A\rightarrow B\rightarrow C$ becomes ambiguous.

For $$A\leftrightarrow B\leftrightarrow C$$ the story is slightly different. There we have that the truth value is independent of the order of evaluation, but both are distinct from the usual interpretation as "$A\leftrightarrow B$ AND $B \leftrightarrow C$".
The relation A -> (B -> C) says that C will come from B if A is present.  This makes no relation between A and B, it can be written as A=Policemen B=naughty boys C=good boys.  The policemen makes naughty boys become good boys.

(A->B) -> C would equate to Policemen make naughty boys, which give good boys as a result.