A surface force apparatus was used to study surface shape changes during the adhesion and spreading of a polymer melt on a bare mica surface. Transient fingers were observed during the initial, rapid spreading process, pointing radially out from the initial adhesive contact point. The fingers had microscopic widths and lengths but submicroscopic thicknesses. They eventually disappeared, leaving a more slowly growing circular neck with a smooth, featureless polymer-air surface. The mean radius of the spreading meniscus (neck) was found to follow a scaling relationship with time of the form (r(i) + r(o))/2 proportional to t(n), with n = 0.128, while the ends of the fingers grew according to r(o) proportional to t(n), with n = 0.10. These rates agree with the values of n = 0.100-0.125 predicted by classical wetting theories for circular macroscopic droplets (i.e., radially symmetric, without fingers) spreading on a solid surface. The lifetime of the transient fingering patterns increases with the polymer viscosity as tau proportional to eta(n), with n = 2.1 +/- 0.2. A circular trough or depression in the film was observed just beyond where the fingers ended, which appears to be a source of the material for the advancing fingers. In addition, beyond the trough, circular ripples/waves were observed on the polymer melt film surface. Such patterns may arise quite generally whenever a perturbation occurs that changes the local forces, thereby inducing a bulge or depression in a liquid film or surface. Thus, we observe similar fingers and ripples/waves during the spreading of liquid polybutadiene on (the immiscible and more viscous) liquid poly(dimethylsiloxane), suggesting that the phenomenon may exist in various liquid adhesion and spreading situations. For low viscosity liquids such as water and low molecular weight oils, our scaling relations suggest that the transient patterns will exist for only a few microseconds; this is likely the reason for why they have not yet been observed.