Quasi-classical limit of KP hierarchy, $W$-symmetries and free fermions

This paper deals with the dispersionless KP hierarchy from the point of view of quasiclassical limit. Its Lax formalism, W-infinity symmetries, and general solutions are shown to be reproduced from their counterparts in the KP hierarchy in the limit of $\hbar\to0$. Free fermions and bosonized vertex operators play a key role in the description of W-infinity symmetries and general solutions, which is technically very similar to a recent free fermion formalism of $c=1$ matrix models. Bibl. 25 titles.