We study symmetries, invariant solutions, and conservation laws for the dispersionless Veselov--Novikov equation. The emphasis is placed on cases when the {\sc ode}s involved in des\-crip\-ti\-on of the invariant solutions are integrable in quadratures. Then we find some non-invariant solutions, in particular, solutions that are polynomials of an arbitrary degree $N \ge 3$ with respect to the spatial variables. Finally we compute all conservation laws that are associated to cosymmetries of second order.