  The thickness $\theta(G)$ of a graph $G$ is the minimum number of planar
spanning subgraphs into which the graph $G$ can be decomposed. As a topological
invariant of a graph, it is a measurement of the closeness to planarity of a
graph, and it also has important applications to VLSI design. In this paper,
the thickness of graphs that are obtained by vertex-amalgamation and
bar-amalgamation of any two graphs whose thicknesses are known are obtained,
respectively. And the lower and upper bounds for the thickness of graphs that
are obtained by edge-amalgamation and 2-vertex-amalgamation of any two graphs
whose thicknesses are known are also derived, respectively.
